Question

How do you solve the system by the substitution method: `2x+3y=6,x=y-7`?

Answer 1

`x = -3 and y = 4`

Explanation:

`color(blue)(x = (y-7))" larr` this means that `x and (y-7)` are identical.
They are therefore interchangeable and one can replace the other.

`" "2color(blue)(x) +3y =6" "larr` replace x with `color(blue)((y-7))`
`color(white)(......)darr`
`2color(blue)((y-7)) +3y = 6" "larr` only y as a variable

`2y-14 +3y = 6`

`5y = 6+14`

`5y = 20`

`y = 4" "larr` if you know `y`, you can work out `x`

`x = y-7`

`x = 4-7 = -3`

Check:
`2x+3y = 2(-3)+3(4)`

`= -6+12 = 6" "larr` which is correct.