### 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?