Answer
($-\frac{14}{3}$,$-\frac{13}{3}$) or $(-4.67,-4.33)$
Work Step by Step
To solve this system of equations, we use the graphing method
$5x+8y=-58$
$2x+2y=-18$
Taking the first equation, we solve for $y$.
$5x+8y=-58$
$8y=-58-5x$
$y=\frac{-58-5x}{8}$
Find three solutions:
For x=2,
$y=\frac{-58-5x}{8}$
$y=\frac{-58-5(2)}{8}$
$y=-8.5$
For x=0,
$y=\frac{-58-5x}{8}$
$y=\frac{-58-5(0)}{8}$
$y=-7.25$
For x=-2,
$y=\frac{-58-5x}{8}$
$y=\frac{-58-5(-2)}{8}$
$y=-6$
With the three points, $(2,-8.5), (0,-7.25), (-2,-6)$ we can graph the straight line that goes through these points.
Taking the second equation, we solve for $y$.
$2x+2y=-18$
$2y=-18-2x$
$y=\frac{-18-2x}{2}$
Find three solutions:
For x=2,
$y=\frac{-18-2x}{2}$
$y=\frac{-18-2(2)}{2}$
$y=-11$
For x=0,
$y=\frac{-18-2x}{2}$
$y=\frac{-18-2(0)}{2}$
$y=-9$
For x=-2,
$y=\frac{-18-2x}{2}$
$y=\frac{-18-2(-2)}{2}$
$y=-7$
With the three points, $(2,-11), (0,-9), (-2,-7)$ we can graph the straight line that goes through these points.
The intersection point between these two lines is the answer to the system of equations.
