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

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

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

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$1)$ $1)$ , $y = x^{2} - 6 x + 1$ $y=x^2-6x+1$

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

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

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

$- 2 x + 6 = x^{2} - 6 x + 1$ $-2x+6=x^2-6x+1$

$x^{2} - 4 x - 5 = 0$ $x^2-4x-5=0$

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

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

$x-5=0, :. x=5$

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

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

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

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