Question

Decide whether or not the ordered pair is a solution of the system of linear equations. $$\begin{aligned} &-5 x-8 y=28\\\ &9 x-2 y=48 \quad(4,-6) \end{aligned}$$

Short answer

Yes, the ordered pair (4,-6) is indeed a solution to the provided system of linear equations.

Step-by-step solution

Substitute in Equation 1

Substitute the pair (4, -6) into the first equation, this results in: -5(4) - 8(-6) = 28, After simplifying, -20 + 48 = 28 which is 28 = 28. As the Left Hand Side (LHS) equals to the Right Hand Side (RHS), the first equation holds true for (4,-6).

Substitute in Equation 2

Substitute the pair (4, -6) into the second equation, the result of which is: 9(4) - 2(-6) = 48, simplified to 36 + 12 = 48, which is 48 = 48. Once again, the LHS equals the RHS, so the second equation holds true for (4, -6).

Final Verification

As the ordered pair (4,-6) holds true for both equations in the system, it can be concluded that (4, -6) is indeed a solution to the given system of linear equations