Question

How do you solve by substitution `x + 2y = 7` and `2x + y = 8`?

Answer 1

`x + 2y = 7`
`x =color(blue)( 7 - 2y` ..........equation `(1)`

`2x + y = 8`...........equation `(2)`

Substituting equation `(1)` in `(2)` to find `y`:
`2color(blue)((7-2y)) + y = 8`
`14 - 4y + y = 8`
`14 - 3y= 8`
`- 3y= -6`
`y= 6/3 , color(purple)(y= 2`

Substituting `y` in equation `1` to find `x`
`x =7 - 2y`
`x =7 - 2.2 = 7-4`
`color(purple)(x =3`

The solution for the system of equations is
`color(purple)(x = 3 , y=2`