Answer
The solutions are $(-3,14)$ and $(1,2)$.
Work Step by Step
The given system is
$y=4x^2+5x-7$ ...... (1)
$y=-3x+5$ ...... (2)
Graph each equation.
The point of intersections are $A=(-3,14)$ and $B=(1,2)$.
Check: $(x,y)=(-3,14)$
Equation (1).
$\Rightarrow y=4x^2+5x-7$
$\Rightarrow 14=4(-3)^2+5(-3)-7$
$\Rightarrow 14=36-15-7$
$\Rightarrow 14=36-22$
$\Rightarrow 14=14$
True.
Equation (2).
$\Rightarrow y=-3x+5$
$\Rightarrow 14=-3(-3)+5$
$\Rightarrow 14=9+5$
$\Rightarrow 14=14$
True.
Check: $(x,y)=(1,2)$
Equation (1).
$\Rightarrow y=4x^2+5x-7$
$\Rightarrow 2=4(1)^2+5(1)-7$
$\Rightarrow 2=4+5-7$
$\Rightarrow 2=9-7$
$\Rightarrow 2=2$
True.
Equation (2).
$\Rightarrow y=-3x+5$
$\Rightarrow 2=-3(1)+5$
$\Rightarrow 2=-3+5$
$\Rightarrow 2=2$
True.
Hence, the solutions are $(-3,14)$ and $(1,2)$.
