Question

Courtney believes that, given a system of two linear equations in two variables, replacing one equation produces a system with the same solution. Test Courtney's conjecture by completing the parts below.

Part A: Verify that the system of equations 3x – 7y = 26 and 5x + 2y = 16 has a solution of (4, -2) by substituting equations and simplifying.

Answer 1

The solution (4, -2) when substituted into both equations 3x – 7y = 26 and 5x + 2y = 16, satisfies them, confirming that this is indeed the solution to the system of linear equations.

Step-by-step explanation:

To verify Courtney's conjecture about the system of linear equations, let's first test if the solution (4, -2) satisfies both equations in the original system, which are 3x – 7y = 26 and 5x + 2y = 16. Substituting x with 4 and y with -2 into each equation, we should determine if the left-hand side equals the right-hand side.

For the first equation (3x – 7y = 26):

3(4) – 7(-2) = 12 + 14 = 26,

which matches the right-hand side, so the first equation is satisfied.

For the second equation (5x + 2y = 16):

5(4) + 2(-2) = 20 - 4 = 16,

which also matches the right-hand side, so the second equation is satisfied as well.

Thus, the solution (4, -2) satisfies both equations in the system, confirming that these equations have a common solution.