Question

Decide whether or not the ordered pair is a solution of the system of linear equations. $$\begin{aligned} &2 x+6 y=22\\\ &-x-4 y=-13 \quad(-5,-2) \end{aligned}$$

Short answer

No, the ordered pair (-5,-2) is not a solution to the system of linear equations.

Step-by-step solution

Substitute in first equation

Substitute the values of x as -5 and y as -2 in the first equation \(2x + 6y = 22\). It becomes \(2*(-5) + 6*(-2) = 22\), simplifying this, we get -10 -12 = 22, which is -22 ≠ 22. So, the left and right sides are not equal.

Conclusion

Since the left and right sides are not equal in the first equation, we conclude that the ordered pair (-5,-2) is not a solution to the system of linear equations. As such, there is no need to substitute into the second equation - once one equation doesn't hold, the pair is not a solution.