Question

Solve the systems of equations below using substitution.

Answer 1

(24,41)

Explanation:

Set the 2 equations equal to each other.

3x - 31 = -2x + 89 Add 2x to both sides of the equal sign

3x + 2x -31 = -2x + 2x + 89

5x -31 = 89 Add 31 to both sides of the equal sign

5x -31 + 31 = 89 + 31

5x = 120 Divide both sides by 5

`(5x)/(5)` =
`(120)/(5)`

x = 24 This is your x value.

Substitute 24 for x into either of the two original equations to solve for y.

y = 3x -31

y = 3(24) - 31

y = 72 - 31

y = 41 This is your y value.

Check:

y = 3x -31

41 = 3(24) - 31

41 = 72 -31

41 = 41 Checks

y = -2x + 89

41 = -2(24) + 89

41 = -48 + 89

41 = 41 Checks.

Answer 2

(24, 41 )

Explanation:

y = 3x - 31 → (1)

y = - 2x + 89 → (2)

substitute y = 3x - 31 into (2)

3x - 31 = - 2x + 89 ( add 2x to both sides )

5x - 31 = 89 ( add 31 to both sides )

5x = 120 ( divide both sides by 5 )

x = 24

substitute x = 24 into either of the 2 equations and solve for y

substituting into (1)

y = 3(24) - 31 = 72 - 31 = 41

solution is (24, 41 )