Question

How do I solve this system of equations and check algebraically?

y=x^2-6x+1
y+2x=6

Answer 1

The basic plan would be to solve one equation for y, and substitute that y value into the other equation and solve the quadratic by factoring preferably and check for extraneous solutions, see below:

Explanation:

`y=x^2-6x+1`
`y+2x=6`
Solve for y:
`y=-2x+6`
Substitute:
`(-2x+6)=x^2-6x+1`
Set the quadratic equal to 0:
`x^2-4x-5=0`
Solve the quadratic by factoring:
`(x-5)(x+1)=0`
Therefore:
`x=5`
`x=-1`
Let us solve for the y-values for each x by substitution:
`y=-2(5)+6`
`y=-4`
`y=-2(-1)+6`
`y=8`
Let's see which one of those coordinate pairs hold true in the quadratic:
`8=(-1)^2-6(-1)+1`
`8=8`
(-1,8) is a true solution
`-4=(5)^2-6(5)+1`
`-4=-4`
(5,-4) is also a true solution