Can someone please help me with this system of equations?

find the exact solution and then check algebraically
1)y=x^2-6x+1
y+2x=6

1 Answer
Apr 4, 2018

x=5, y=-4x=5,y=4

x=-1, y=8x=1,y=8

Explanation:

.

1)1), y=x^2-6x+1y=x26x+1

2)2), y+2x=6y+2x=6

We solve for yy from the second equation and substitute it into the first equation:

y=-2x+6y=2x+6

-2x+6=x^2-6x+12x+6=x26x+1

x^2-4x-5=0x24x5=0

We can solve for xx by either using the quadratic formula or factoring if the expression is factorable. This equation is factorable:

(x-5)(x+1)=0(x5)(x+1)=0

x-5=0, :. x=5

x+1=0, :. x=-1

Now, we will plug each x into either of the original equations and solve for y. We will have two sets of solutions:

x=5, :. y=-2x+6=-2(5)+6=-10+6=-4

x=-1, :. y=-2x+6=-2(-1)+6=2+6=8