Answer
No real solution
Work Step by Step
Given$$
\begin{cases}
y&=x^2+5 x-3 \\
y&=2 x-10.
\end{cases}
$$ Set the two equations equal and solve for the values of $x$.
$$
\begin{aligned}
x^2+5 x-3 & =2 x-10 \\
x^2+5 x-2 x & =3-10 \\
x^2+3 x & =-7 \\
x^2+3 x+\left(\frac{3}{2}\right)^2 & =-7+\left(\frac{3}{2}\right)^2 \\
\left(x+\frac{3}{2}\right)^2 & =-\frac{7 \cdot 4+9}{4} \\
\left(x+\frac{3}{2}\right)^2 & =-\frac{37}{4}.
\end{aligned}
$$ The equation has no real solution.
