Answer
The solutions are $(\frac{1}{3},-\frac{7}{3})$ and $(-\frac{2}{3},-\frac{22}{3})$.
Work Step by Step
The given system is
$y=9x^2+8x-6$ ...... (1)
$y=5x-4$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=9x^2+8x-6-(5x-4)$
$\Rightarrow y-y=9x^2+8x-6-5x+4$
Simplify.
$\Rightarrow 0=9x^2+3x-2$
Factor the polynomial.
$\Rightarrow 0=(3x-1)(3x+2)$
Use zero product property.
$\Rightarrow 3x-1=0$ or $3x+2=0$
Solve for $x$.
$\Rightarrow x=\frac{1}{3}$ or $x=-\frac{2}{3}$
Substitute $\frac{1}{3}$ for $x$ in equation (2).
$\Rightarrow y=5(\frac{1}{3})-4$
Simplify.
$\Rightarrow y=\frac{5}{3}-4$
$\Rightarrow y=\frac{5-12}{3}$
$\Rightarrow y=-\frac{7}{3}$
Substitute $-\frac{2}{3}$ for $x$ in equation (2).
$\Rightarrow y=5(-\frac{2}{3})-4$
Simplify.
$\Rightarrow y=-\frac{10}{3}-4$
$\Rightarrow y=\frac{-10-12}{3}$
$\Rightarrow y=-\frac{22}{3}$
Hence, the solutions are $(\frac{1}{3},-\frac{7}{3})$ and $(-\frac{2}{3},-\frac{22}{3})$.
