Question

How do you solve the system `2x = 3 - y` and `2y = 12 - x` by substitution?

Answer 1

`2x = 3 - y`
`y = 3 - 2x`............equation `(1)`

`2y = 12 - x` ........equation `(2)`

substituting equation `(1)` in equation `(2)`
`2(3-2x) = 12 - x`
`6 - 4x = 12 - x`
`-6 = 3x`
`x =-2`

finding `y` :
`y = 3 - 2x` , from equation `(1)`
`= 3 - 2(-2)`
`= 3+4 = 7`

solutions for the system of equations are
`color (blue)(x=-2 and y = 7`