### Home > AC > Chapter 7 > Lesson 7.1.4 > Problem7-38

7-38.

Find the point of intersection for each system of linear equations below. Be sure to check your solutions. Which method did you use for each system and why?

1. \begin{aligned} [t] 5x-y&=2\\ 3x+y&=-10\end{aligned}

Use the Elimination Method.

The result is: $8x = −8$

Solve for $x$ by dividing the equation by $8$. $x = −1$

Substitute $x$ into one of the original equations to find $y$. $5\left(−1\right) − y = 2$

Solve for $y$.
$y = −7$

$\left(−1, −7\right)$

1. \begin{aligned} [t] 6x+2y&=7\\ 4x+y&=4\end{aligned}

Use the Elimination Method.

Multiply the 2nd equation by $−2$

Follow the steps outlined in part (a).

1. \begin{aligned} [t] 5x+2y&=7\\ 2y+5x&=7\end{aligned}

Try rewriting the 2nd equation. What do you notice?