Question

How do you solve `7x - y = 26` and `x + y = 6` using substitution?

Answer 1

The solution for the system of equations is :
`color(green)(x= 4`

`color(green)(y=2`

Explanation:

`7x - y = 26`.........equation `(1)`

`x + y = 6`,
`color(blue)(y = 6 - x`..............equation `(2)`

Solving by substitution :

Substituting equation `2` in equation `1`:

`7x - y = 26`

`7x - color(blue)((6 - x))= 26`

`7x - 6 + x= 26`

`7x + x= 26 + 6`

`8x= 32`

`x= 32/8`

`color(green)(x= 4`

Finding `y` from equation `2`
`color(blue)(y = 6 - x`

`y = 6 - 4`

`color(green)(y=2`

The solution for the system of equations is :
`color(green)(x= 4`

`color(green)(y=2`