Answer
$(-39.11,183.52)$, $(1.11,2.48)$
Work Step by Step
Given $$
\begin{cases}
& y=0.25 x^2+5 x-3.4 \\
& y=-4.5 x+7.5.
\end{cases}
$$ Set the two equations equal and solve for the values of $x$.
$$
\begin{aligned}
\frac{0.25 x^2}{0.25}+\frac{5 x}{0.25}-\frac{3.4}{0.25} & =-\frac{4.5 x}{0.25}+\frac{7.5}{0.25} \\
x^2+20 x-13.6 & =-18 x+30 \\
x^2+20 x+18 x & =30+13.6 \\
x^2+38 x+19^2 & =43.6+19^2 \\
(x+19)^2 & =404.6\\
x+19 & = \pm \sqrt{404.6} \\
x & =-19 \pm \sqrt{404.6}
\end{aligned}
$$ The solution is: $$
\begin{aligned}
x & =-19-\sqrt{404,6} \\
& \approx39.11467 \\
x & =-19+\sqrt{404.6} \\
& \approx 1.11467
\end{aligned}
$$ Find the corresponding $y$ values using either of the given equations.$$
\begin{aligned}
y&=-4.5 (-39.11467)+7.5\\
& \approx 183.516\\
y&=-4.5 (1.11467)+7.5\\
& \approx 2.484.
\end{aligned}
$$ Plot the two functions in the same window to check the solution(s).
