Question

The pair of linear equations is graphed below.

Which values for x and y will satisfy both linear equations?

x = 0, y = 7

x = – 7, y = 0

x = 3, y = – 4

x = – 4, y = 3

Answer 1

(-4,3)

x = -4 and y = 3

Explanation:

Set the two equation equal to each other and solve for x.

x + 7 =
`(3)/(4)` x + 6 Multiply all the way through by 4 to clear the fraction

4(x + 7) = 4(
`(3)/(4)` x + 6) Distribute the 4

4x + 4(7) = 4(
`(3)/(4)`x) + 4(6)

4x + 28 = 3x + 24
`(4)/(1)` x
`(3)/(4)` =
`(12)/(4)` = 3 (
`(4)/(1)` is another name for 4) subtract 3x from both sides

4x - 3x + 28 = 3x - 3x + 24

x + 28 = 24 subtract 28 from both sides

x + 28 - 28 = 24 - 28

x = -4

Substitute -4 for x in either of the two original equations and solve for y.

y = x + 7

y = -4 + 7

y = 3

Check

Substitute in -4 for x and 3 for y and see if we get true statements.

y = x + 7

3 = -4 + 7

3 = 3 checks

y =
`(3)/(4)` x + 6

3 =
`(3)/(4)`
`((-4)/(1))` + 6

3 = -3 + 6

3 = 3 cfhecks