### Home > CAAC > Chapter 7 > Lesson 7.3.1 > Problem 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. Homework Help ✎

*y*= 2*x*− 3

*x*−*y*= −4*y*−*x*= −2

−3*y*+ 2*x*= 14

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

*y* = 2*x* − 3. Substitute *y*:*x* − *y* = −4*x* − (2*x*−3) = −4

Solve for *x*.

Distribute the left side.

*x* − 2*x* + 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

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

Multiply the top equation by 2.

2(*y* − *x* = − 2)

2*y* − 2*x* = −2

Add the two equations together by combining like terms.

2*y* − 2*x* = −4

−3*y* + 2*x* = 14

−*y* + 0 = 10

Solve for *y*.

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

Don't forget to check your solution!