Question

How do you solve the system `4x+3y=17` and `y=-2x+11`?

Answer 1

The values for `(x,y)` are `(8,-5)`

Explanation:

`4x+3y=17`
`y=-2x+11`

For the solution of this system of equations we can use the substitution method since the y variable is already isolated in the second equation.

We can take the value for y in the second equation and plug it in for the y in the first equation. This means we will only be solving for the `x` variable.

`4x+3y=17`
`4x+3(-2x+11)=17`
`4x-6x+33=17`
`-2x+cancel33-cancel33=17 -33`
`-2x=-16`
`(cancel(-2)x)/(cancel(-2))=-16/-2`
`x=8`

Now plug the `x` value back in the original equations to solve for `y`

`y=-2x+11`
`y=-2(8)+11`
`y=-16+11`
`y=-5`

the values for `(x,y)` are `(8,-5)`