18. Systems of Equations and Matrices

Two Variable Systems of Linear Equations

18. Systems of Equations and Matrices

Two Variable Systems of Linear Equations

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$y=5x-17$
$15x-3y=51$

Consistent and Independent

Consistent and Dependent

Inconsistent

Verified step by step guidance

Step 1: Start by examining the given system of equations. The first equation is y = 5x - 17, and the second equation is 15x - 3y = 51.

Step 2: Substitute the expression for y from the first equation into the second equation. This means replacing y in the second equation with 5x - 17.

Step 3: Simplify the second equation after substitution. Distribute and combine like terms to see if the equation holds true or results in a contradiction.

Step 4: Analyze the resulting equation. If it simplifies to a true statement (like 0 = 0), the system is consistent and dependent. If it simplifies to a false statement (like 0 = 5), the system is inconsistent.

Step 5: If the equations are consistent and dependent, it means they represent the same line, and there are infinitely many solutions. If they are consistent and independent, they intersect at a single point.