### Home > AC > Chapter 7 > Lesson 7.1.2 > Problem7-16

7-16.

Find the solution for each system of equations below, if a solution exists. If there is not a single solution, explain why not. Be sure to check your solution, if possible.

1. \begin{aligned}[t] &x + 4y = 2 \\ &3x - 4y = 10 \end{aligned}

Since $x$ represents the same number in the first equation as it does in the second, as does $y$, and the same operations are being carried out, the equations would have to equal the same number.

No solution

1. \begin{aligned}[t] &2x + 4y = -10 \\ &x = -2y - 5 \end{aligned}

Can you multiply both sides of the second equation by anything to get the first? If so, the equations will be the same.