Answer
$(5,1),(-1,7)$
Work Step by Step
$y=x^{2}-5x+1$ Equation $(1)$
$y=-x+6$ Equation $(2)$
From Equation $(1)$ and Equation $(2)$
$x^{2}-5x+1=-x+6$
$x^{2}-5x+1+x-6=0$
$x^{2}-4x-5=0$
By factoring,
$(x-5)(x+1)=0$
$x=5$ or $x=-1$
Substitute $x$ values in Equation $(2)$ to get corresponding $y$ values.
Let $x=5$
$y=-x+6$
$y=-5+6$
$y=1$
Let $x=-1$
$y=-x+6$
$y=-(-1)+6$
$y=1+6$
$y=7$
$(5,1),(-1,7)$ satisfy the given equations.
The solution set is $\{(5,1),(-1,7)\}$
