Question

How do you solve the system of equations `2a + 2x = 18` and `a + 3x = 17`?

Answer 1

`a=5` and `x=4`

Explanation:

`2a+2x=18`
`a+3x=17`

Reduce the first equation by dividing all terms by `2`.

`2a+2x=18`

`a+x=9`

Subtract `x` from each side.

`a=9-x`

In the second equation, replace `a` with `color(red)((9-x))`.

`a+3x=17`

`color(red)((9-x))+3x=17`

Open the brackets and simplify.

`9-x+3x=17`

`9+2x=17`

Subtract `9` from both sides.

`2x=8`

Divide both sides by `2`.

`x=4`

In the second equation, replace `x` with `color(blue)4`.

`a+3x=17`

`a+3xxcolor(blue)4=17`

`a+12=17`

Subtract `12` from both sides.

`a=5`