### Home > GC > Chapter 7 > Lesson 7.1.1 > Problem7-10

7-10.

Solve each system of equations below, if possible. If it is not possible, explain what the lack of an algebraic solution tells you about the graphs of the equations. Write each solution in the form $(x,y)$. Show all work.

1. $y=-2x-1$
$y=\frac{1}{2}x-16$

By the Equal Values Method,

$-2x-1=\frac{1}{2}x-16$

$x=6$

Substitute $6$ for $x$ in one of the original equations.
Solve for $y$, which will give you the intersection of the two lines.

1. $y=x^2+1$
$y=-x^2$

By the Equal Values Method,

$x^2+1=-x^2$

$2x^2+1=0$

By the Quadratic Formula,

$x=\frac{0\pm\sqrt{0^2=(4)(2)(1)}}{2\cdot2}\;\to\;x=\frac{0\pm\sqrt{-8}}{4}$

A negative square root is not possible, so there are no solutions. This means the graphs do not intersect.