Answer
$(-\frac{1}{2},\frac{5}{4})$ or $(-0.5,1.25)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$2x+8y=9$
$4x+4y=3$
Taking the first equation, we solve for y.
$2x+8y=9$
$8y=9-2x$
$y=\frac{9-2x}{8}$
Find three solutions:
For x=2,
$y=\frac{9-2(2)}{8}$
$y=\frac{9-4}{8}$
$y=\frac{5}{8}=0.625$
For x=0,
$y=\frac{9-2(0)}{8}$
$y=\frac{9-0}{8}$
$y=\frac{9}{8}=1.125$
For x=-2,
$y=\frac{9-2(-2)}{8}$
$y=\frac{9+4}{8}$
$y=\frac{13}{8}=1.625$
With the three points, $(2,0.625), (0,1.125), (-2,1.625)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$4x+4y=3$
$4y=3-4x$
$y=\frac{3-4x}{4}$
Find three solutions:
For x=2,
$y=\frac{3-4(2)}{4}$
$y=\frac{3-8}{4}$
$y=\frac{-5}{4}=-1.25$
For x=0,
$y=\frac{3-4(0)}{4}$
$y=\frac{3-0}{4}$
$y=\frac{3}{4}=0.75$
For x=-2,
$y=\frac{3-4(-2)}{4}$
$y=\frac{3+8}{4}$
$y=\frac{11}{4}=2.75$
With the three points, $(2,-1.25), (0,0.75), (-2,2.75)$, 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.
