CPM Homework Help : CAAC Problem 7-87

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. Homework Help ✎
1. y = 2x − 3
  x − y = −4
2. y − x = −2
  −3y + 2x = 14

Hint (a):

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

Step 1(a):

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

Step 2(a):

Solve for x.

Distribute the left side.

x − 2x + 3 = −4

Step 3(a):

Combine like terms.

−x + 3 = −4

Step 4(a):

Subtract 3 on both sides.

−x = −7

Hint (a):

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

Answer (a):

x = 7

y = 11

Hint (b):

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

Step 1(b):

Multiply the top equation by 2.

2(y − x = − 2)
2y − 2x = −2

Step 2(b):

Add the two equations together by combining like terms.

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

Step 3(b):

Solve for y.

Hint (b):

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

Reminder:

Don't forget to check your solution!