Question

How do you solve the system of equations `\frac { 1} { 2} x + y = 4` and `3x - 2y = 8`?

Answer 1

The solution is `x=4` and `y=2`.

Explanation:

Strategy. If you multiply `1/2 x + y=4` by `2`, and then add that to `3x-2y=8`, you can get an equation in terms of `x` only. Solve for `x`, then using the value of `x`, solve for `y`.

Step 1. Multiply by `2` and add the equations

`2(1/2 x + y)=2(4)`

`color(white)(aa|)x+2y=8`
`ul(+3x-2y=8)`
`4x=16`

Dividing both sides by `4` gives

`x=4`

Step 2. Plug `x=4` back into one of the original two equations

`color(red)(x=4)`

`3color(red)(x)-2y=8`

`3(color(red)(4))-2y=8`

`12-2y=8`

Subtract `12` from both sides

`-2y=-4`

Divide both sides by `-2`

`y=2`

The solution is `x=4` and `y=2`.