  ### Home > AC > Chapter 7 > Lesson 7.3.1 > Problem7-87

7-87.

Solve the following systems of equations. Remember to check your solution in both equations to make sure it is the point of intersection.

1. $y=2x−3\\x−y=−4$

One way to solve this system of equations is by using the substitution method.

$y = 2x − 3$. Substitute $y$:
$x − y = −4\\x − \left(2x−3\right) = −4$

Solve for $x$.

Distribute the left side.

$x − 2x + 3 = −4$

Combine like terms.

$−x + 3 = −4$

Subtract $3$ on both sides.

$−x = −7$

Use the solution you found for $x$ and substitute it into either original equation and solve for $y$.

$x = 7$

$y = 11$

1. $y − x = −2\\ −3y + 2x = 14$

One way to solve this system of equations is by using the elimination method.

Multiply the top equation by $2$.

$2\left(y − x = − 2\right)\\2y − 2x = −2$

Add the two equations together by combining like terms.

$2y − 2x = −4\\−3y + 2x = 14\\ −y + 0 = 10$

Solve for $y$.

When you find $y$, you can now substitute the value into either original equation and solve for $x$.

Don't forget to check your solution!