Question

Do you think there are any ordered pairs that are solutions to BOTH y = x + 5 and y = –2x – 1? Explain.

Answer 1

(-2,3)

Explanation:

Set the two equations equal to each other since they both equal y

x + 5 = -2x - 1

+2x +2x Add 2x to both sides

3x + 5 = -1

- 5 - 5 Subtract 5 from both sides

3x = -6 Divide both sides by 3

x = -2

Plug this into one of the original equations

y = x + 5

y = -2 + 5 Add

y = 3

Answer 2

The ordered pair is
`(-2,3)`

Explanation:

`y=x+5\\</p><p>y=-2x-1\\</p><p>\implies x+5=-2x-1\\</p><p>\implies 3x=-6\\</p><p>\boxed{x=-2}\\</p><p>\implies y=-2+5=\boxed {3}\\`