7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

Guided videos.

Learn with Patrick

Go to the course

Guided course

Introduction to Systems of Linear Equations

4:27

Introduction to Systems of Linear Equations

Solving Systems of Equations - Substitution

Solving Systems of Equations - Elimination

How to Multiply Equations in Elimination Method

Classifying Systems of Linear Equations

Showing 9 of 9 videos

Learn with other creators

Solve a Linear System Graphical Approach

5:00

Solve a Linear System Graphical Approach

Solve a Linear System û by the Substitution Method

Solve a Linear System û by the Elimination Method

Practice this topic

Multiple Choice

Use substitution to solve the following system of linear equations.

$4x+y=1$

$x-y=4$

Use substitution to solve the following system of linear equations.

$4x+2y=7$

$x+5y=4$

Use the elimination method to solve the following system of linear equations.

$2x+y=1$

$3x-y=4$

Use the elimination method to solve the following system of linear equations.

$10x-4y=5$

$5x-4y=1$

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.

$y=5x-17$

$15x-3y=51$

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.

$2x+8y=7$

$x+4y=19$

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 2x + 6y = 6 5x + 9y = 9

276

views

Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13

465

views

Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

340

views

Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (- 3, 5) 9x + 7y = 8 8x - 9y = - 69

281

views

Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

247

views

Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

247

views

Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x + 4y = 16

In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x

263

views

Textbook Question

A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

458

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9

229

views

Textbook Question

Solve each system by substitution. See Example 1. 4x + 3y = -13 -x + y = 5

Solve each system by substitution. See Example 1. x - 5y = 8 x = 6y

263

views

Textbook Question

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.

196

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. x = 4y - 2 x = 6y + 8

311

views

Textbook Question

Solve each problem. Alcohol MixtureBarak wishes to strengthen a mixture that is 10% alcohol to onethat is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?

169

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

242

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

242

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. 2x + 5y = - 4 3x - y = 11

229

views

Textbook Question

Solve each system by substitution. See Example 1. 7x - y = -10 3y - x = 10

235

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. 2x - 3y = 8 - 2x 3x + 4y = x + 3y + 14

271

views

Textbook Question

Solve each system by substitution. See Example 1. -2x = 6y + 18 -29 = 5y - 3x

300

views

Textbook Question

Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

175

views

Textbook Question

In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2

200

views

Textbook Question

Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2

254

views

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 4x + y = -23 x - 2y = -17

155

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3

271

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

251

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

251

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

275

views

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 5x + 7y = 6 10x - 3y = 46

192

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. 4x + 3y = 15 2x - 5y = 1

202

views

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 6x + 7y + 2 = 0 7x - 6y - 26 = 0

415

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4

240

views

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. x/2+ y/3 = 4 3x/2+3y/2 = 15

179

views

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. (2x-1)/3 + (y+2)/4 = 4 (x+3)/2 - (x-y)/2 = 3

280

views

Textbook Question

In Exercises 19–30, solve each system by the addition method. 3x = 4y + 1 3y = 1 - 4x

210

views

Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2y x + 2y = 13

234

views

Textbook Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4. 9x - 5y = 1 -18x + 10y = 1

Determine the system of equations illustrated in each graph. Write equations in standard form.

271

views

Textbook Question

Determine the system of equations illustrated in each graph. Write equations in standard form.

240

views

Textbook Question

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

205

views

Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2

275

views

Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3

183

views

Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3

183

views

Textbook Question

In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

300

views

Textbook Question

Solve each system. (Hint: In Exercises 69–72, let 1/x = t and 1/y = u.) 2/x + 3/y = 18 4/x - 5/y = -8

157

views

Textbook Question

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

175

views

Textbook Question

For what value(s) of k will the following system of linear equations have no solution? infinitely many solutions? x - 2y = 3 -2x + 4y = k

316

views

Textbook Question

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 50% alcohol solution must be mixed with 80 ounces of a 20% alcohol solution to make a 40% alcohol solution?

183

views

Textbook Question

Use a system of equations to solve each problem. See Example 8. Find an equation of the line y = ax + b that passes through the points (-2, 1) and (-1, -2).

245

views

Textbook Question

Use a system of equations to solve each problem. See Example 8. Find an equation of the parabola y = ax^2 + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).

230

views

Textbook Question

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

190

views

Textbook Question

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

190

views

Textbook Question

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

Solve the systems in Exercises 79–80. log x^2=y+3, log x=y−1

views

Textbook Question

Solve the systems in Exercises 79–80. log_y x=3, log_y (4x)=5

views

Textbook Question

Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.

views

Textbook Question

Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.

views

Textbook Question

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. The difference between the squares of two numbers is 3. Twice the square of the first number increased by the square of the second number is 9. Find the numbers.

views

Textbook Question

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. The sum of two numbers is 10 and their product is 24. Find the numbers.

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. x^2+y^2+3y=22, 2x+y=−1

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. y=(x+3)^2, x+2y=−2

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. x^2+(y−2)^2=4, x^2−2y=0

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. x^3+y=0, x^2−y=0

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. x^2+4y^2=20, x+2y=6

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. 2x^2+y^2=18, xy=4

views

Textbook Question

In Exercises 29–42, solve each system by the method of your choice. 3x^2+4y^2=16, 2x^2−3y^2=5

views

Textbook Question

In Exercises 19–28, solve each system by the addition method. y^2−x=4, x^2+y^2=4

views

Textbook Question

In Exercises 19–28, solve each system by the addition method. x^2+y^2=25, (x−8)^2+y^2=41

views

Textbook Question

In Exercises 19–28, solve each system by the addition method. 3x^2+4y^2−16=0, 2x^2−3y^2−5=0

views

Textbook Question

In Exercises 19–28, solve each system by the addition method. x^2−4y^2=−7, 3x^2+y^2=31

views

Textbook Question

In Exercises 47–52, solve each system by the method of your choice. 3/x^2+1/y^2=7, 5/x^2−2/y^2=−3

views

Textbook Question

In Exercises 47–52, solve each system by the method of your choice. −4x+y=12, y=x^3+3x^2

views

Textbook Question

In Exercises 19–28, solve each system by the addition method. x^2+y^2=13,x^2−y^2=5

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. x+y=1, (x-1)^2+(y+2)^2=10

115

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. x+y=1, x^2+xy-y^2=-5

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. xy=3, x^2+y^2=10

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. y^2=x^2-9, 2y=x-3

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. xy=6, 2x-y=1

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. x^2+y^2=25, x-y=1

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. y=x^2-4x-10, y=-x^2-2x+14

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. x+y=2, y=x^2-4x+4

views

Textbook Question

In Exercises 1–18, solve each system by the substitution method. x+y=2, y=x^2−4

views

Textbook Question

The perimeter of a rectangle is 26 meters and its area is 40 square meters. Find its dimensions.

292

views

Textbook Question

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

views

Textbook Question

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

views

Textbook Question

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

views

Textbook Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____). x + y = 7 x^2 + y^2 = 25

views

Textbook Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (___, 3). 2x + y = 1 x^2 + y^2 = 10

views

Textbook Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)? x^2 + y = 2 (1) x - y = 0 (2)

views

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose sum is 17 and whose product is 42.

views

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose squares have a sum of 100 and a difference of 28.

views

Textbook Question

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations. 2x^2 = 3y + 23 y = 2x - 5

views

Textbook Question

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations. y = 3x^2 x^2 + y^2 = 10

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. x^2 - y = 0 x + y = 2

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. y = x^2 - 2x + 1 x - 3y = -1

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. y = x^2 + 6x + 9 x + 2y = -2

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. y = 6x + x^2 4x - y = -3

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. x^2 + y^2 = 5 -3x + 4y = 2

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. x^2 + y^2 = 10 2x^2 - y^2 = 17

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. x^2 + y^2 = 0 2x^2 - 3y^2 = 0

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. x^2 + 2y^2 = 9 x^2 + y^2 = 25

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. 3x^2 + 5y^2 = 17 2x^2 - 3y^2 = 5

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. 5x^2 - 2y^2 = 25 10x^2 + y^2 = 50

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. 2xy + 1 = 0 x + 16y = 2

views

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. 3x^2 - y^2 = 11 xy = 12

views

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

views

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

views

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

views

Textbook Question

Answer each question. Does the straight line 3x - 2y = 9 intersect the circle x^2 + y^2 = 25? (Hint: To find out, solve the system formed by these two equations.)

views

Textbook Question

Answer each question. A line passes through the points of intersection of the graphs of y = x^2 and x^2 + y^2 = 90. What is the equation of this line?

views

Textbook Question

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.^3 and lateral surface area 65 in.^2.

views

Textbook Question

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = 2000/(2000 - q) and demand: p = (7000 - 3q)/2q Find the equilibrium demand.

views

Textbook Question

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = 2000/(2000 - q) and demand: p = (7000 - 3q)/2q Find the equilibrium price (in dollars).

views

Textbook Question

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q) Find the equilibrium demand.

views

Textbook Question

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q) Find the equilibrium price (in dollars).

views

Textbook Question

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x^2 + y^2 = 25 at only one point.

views

Textbook Question

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x^2 + y^2 = 20 and x^2 - y = 0.

views

Textbook Question

In Exercises 47–52, solve each system by the method of your choice. 2x^2+xy=6, x^2+2xy=0

views

Showing 135 of 135 practice

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

Learn with Patrick

Learn with other creators

Practice this topic