### Home > CCG > Chapter Ch7 > Lesson 7.1.1 > Problem7-11

7-11.

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. \begin{aligned}[t] &y = -2x - 1 \\ &y = \frac{1}{2}x - 16 \end{aligned}

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. \begin{aligned}[t] &y = x^2 + 1 \\ &y = -x^2 \end{aligned}

By the Equal Values Method,

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

$2x^2+1=0$

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