Question

How do you solve the system of equations `5x - 7y = 16` and `- x + 7y = 8`?

Answer 1

`(x,y)=(6,2)`

Explanation:

We can solve this system by noticing that the `y` terms are `-7y` and `7y` - and so we can add the two equations together, eliminate the `y` term, solve for `x`, then go back and solve for `y`:

`color(white)(-)5x-7y=16`
`ul(-color(white)(05)x+7y=color(white)(0)8`
`color(white)(000)4x+0y=24`

`=> 4x=24=> color(blue)(ul(bar(abs(color(black)(x=6))))`

We can now plug our `x` value into any of the original equations to find `y`:

`-x+7y=8`

`-6+7y=8`

`7y=14=>color(blue)(ul(bar(abs(color(black)(y=2))))`

And we can see this in the graph of the two lines:

graph{(5x-7y-16)(-x+7y-8)=0 [-3.5, 16.5, -2.6, 7.4]}