Question

How do you solve the system of equations `2x + 8y = 10` and `2x + y = 17`?

Answer 1

`x=9`
`y=-1`

Explanation:

`2x + 8y = 10`
`2x + y = 17`

`2x + 8y = 10`
`-1(2x + y = 17)`

`2x + 8y = 10`
`-2x - y = -17`

now add the equations together:

`7y = -7`

`y=-1`

Use either of the 2 original equations with your `y` value to solve for `x`:

`2x + y = 17`

`2x + (-1) = 17`

`2x = 18`

`x=9`

Answer 2

The solution is `(9,-1)`.

Explanation:

`"Equation 1":` `2x+8y=10`

`"Equation 2":` `2x+y=17`

The solution to a system of linear equations is the point or points they have in common. I'm going to solve the system by elimination.

Multiply Equation 1 by `-1`. This will reverse the signs.

`-2x-8y=-10`

Add Equation 1 to Equation 2.

`color(white)(..)2x+color(white)(.)y=color(white)(..)17`
`-2x-8y=-10`
`-------------`
`color(white)(.......)-7y=color(white)(....)7`

Divide both sides by `-7`.

`y=-7/7`

`y=-1`

Substitute `-1` for `y` in Equation 2 and solve for `x`.

`2x-1=17`

Add `1` to both sides.

`2x=17+1`

`2x=18`

Divide both sides by `2`.

`x=18/2`

`x=9`

The solution is `(9,-1)`.

graph{(2x+8y-10)(2x+y-17)=0 [-4.25, 15.75, -5.04, 4.96]}