Question

How do you solve the system of equations `y= x + 2` and `y = - 2x + 2y`?

Answer 1

`x=2,y=4`

Explanation:

`color(red)(y=x+2)---(1)`

`y=-2x+2y---(2)`

perhaps teh quickest way is to substitute `(1)" into "(2)`

`color(red)(x+2)=-2x+2color(red)((x+2))`

`x+2=cancel(-2x+2x)+4`

`:.x=2`

`(1)rarry=2+2=4`

`x=2,y=4`

a quick mental check with #(2) confirms the consistency of soln.

Answer 2

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y`, substitute `(x + 2)` for both occurrences of `y` in the second equation and solve for `x`:

`y = -2x + 2y` becomes:

`(x + 2) = -2x + 2(x + 2)`

`x + 2 = -2x + 2x + 4`

`x + 2 = 0 + 4`

`x + 2 = 4`

`x + 2 - color(red)(2) = 4 - color(red)(2)`

`x + 0 = 2`

`x = 2`

Step 2) Substitute `2` for `x` in the first equation and calculate `y`:

`y = x + 2` becomes:

`y = 2 + 2`

`y = 4`

The Solution Is:

`x = 2` and `y = 4`

Or

`(2, 4)`