Solve each system in Exercises 5–18. 2x+y=2, x+y−z=4, 3x+2y+z=0
Verified step by step guidance
1
Step 1: Start by labeling the equations for clarity: Equation 1: , Equation 2: , Equation 3: .
Step 2: Use Equation 1 to express in terms of : .
Step 3: Substitute into Equation 2: , and simplify to find in terms of .
Step 4: Substitute into Equation 3: , and simplify to find in terms of .
Step 5: Solve the simplified equations from Steps 3 and 4 simultaneously to find the values of , , and .
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Equations
A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. Methods to solve these systems include substitution, elimination, and matrix operations, each providing a way to find the intersection of the equations' graphs.
The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equations. This reduces the number of equations and variables, making it easier to find the solution. It is particularly useful when one equation is easily solvable for a single variable.
The elimination method, also known as the addition method, involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variables. This method is effective when the coefficients of one variable are opposites or can be made opposites through multiplication, simplifying the process of finding the solution.