Answer
The solutions are $(-1,6)$ and $(2,9)$.
Work Step by Step
The given system is
$y=3x^2-2x+1$ ...... (1)
$y=x+7$ ...... (2)
Graph each equation.
The point of intersections are $A=(-1,6)$ and $B=(2,9)$.
Check: $(x,y)=(-1,6)$
Equation (1).
$\Rightarrow y=3x^2-2x+1$
$\Rightarrow 6=3(-1)^2-2(-1)+1$
$\Rightarrow 6=3+2+1$
$\Rightarrow 6=6$
True.
Equation (2).
$\Rightarrow y=x+7$
$\Rightarrow 6=-1+7$
$\Rightarrow 6=6$
True.
Check: $(x,y)=(2,9)$
Equation (1).
$\Rightarrow y=3x^2-2x+1$
$\Rightarrow 9=3(2)^2-2(2)+1$
$\Rightarrow 9=12-4+1$
$\Rightarrow 9=13-4$
$\Rightarrow 9=9$
True.
Equation (2).
$\Rightarrow y=x+7$
$\Rightarrow 9=2+7$
$\Rightarrow 9=9$
True.
Hence, the solutions are $(-1,6)$ and $(2,9)$.
