Can someone please help me with this system of equations?

Question

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

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Answer 1 · 2018-04-04T16:30:55

#x=5, y=-4#

#x=-1, y=8#

.

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

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

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

#y=-2x+6#

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

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

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

#(x-5)(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#