Question

How do you solve the system `y=2-x` and `5=y+2x` using substitution?

Answer 1

`y=2-x` --------------(1)

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

Substituting `y` from the first equation into the second one gives us:

`5 = (2-x) + 2x`

`5 = 2 - x + 2x`

`5 = 2 + x`

Transposing 2 to the left hand side gives us :

`5-2 = x`

`color(green)(x = 3`

Substituting `x = 3` in the first equation will give us :

`y = 2 - 3`

`color(green)(y = -1`

The solution to both these equations :`x = 3; y = -1`

Verify :

Substitute the values of `x and y` in both the equations to see if they are satisfied