Answer
$(\frac{1}{4},\frac{2}{3})$ or $(0.25, 0.67)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$8x-3y=0$
$4x+3y=3$
Taking the first equation, we solve for y.
$8x-3y=0$
$-3y=0-8x$
$y=\frac{-8x}{-3}$
$y=\frac{8x}{3}$
Find three solutions:
For x=2,
$y=\frac{8x}{3}$
$y=\frac{8(2)}{3}$
$y\approx5.33$
For x=0,
$y=\frac{8x}{3}$
$y=\frac{8(0)}{3}$
$y=0$
For x=-2,
$y=\frac{8x}{3}$
$y=\frac{8(-2)}{3}$
$y\approx-5.33$
With the three points, $(2,5.33), (0,0), (-2,-5.33)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$4x+3y=3$
$3y=3-4x$
$y=\frac{3-4x}{3}$
Find three solutions:
For x=2,
$y=\frac{3-4(2)}{3}$
$y=\frac{3-8}{3}$
$y=\frac{-5}{3}\approx-1.67$
For x=0,
$y=\frac{3-4(0)}{3}$
$y=\frac{3-0}{3}$
$y=\frac{3}{3}=1$
For x=-2,
$y=\frac{3-4(-2)}{3}$
$y=\frac{3+8}{3}$
$y=\frac{11}{3}\approx3.67$
With the three points, $(2,-1.67), (0,1), (-2,3.67)$, 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.
