Answer
$(4,0)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$6x+2y=24$
$3x-4y=12$
Taking the first equation, we solve for y.
$6x+2y=24$
$2y=24-6x$
$y=\frac{24-6x}{2}$
$y=12-3x$
Find three solutions:
For x=2,
$y=12-3(2)$
$y=12-6$
$y=6$
For x=0,
$y=12-3(0)$
$y=12-0$
$y=12$
For x=-2,
$y=12-3(-2)$
$y=12+6$
$y=18$
With the three points, $(2,6), (0,12) (-2,18)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for $y$.
$3x-4y=12$
$-4y=12-3x$
$y=\frac{12-3x}{-4}$
Find three solutions:
For $x=2$,
$y=\frac{12-3(2)}{-4}$
$y=\frac{12-6}{-4}$
$y=-\frac{6}{4}=-1.5$
For $x=0$,
$y=\frac{12-3(0)}{-4}$
$y=\frac{-12-0}{-4}$
$y=\frac{-12}{-4}=3$
For $x=-2$,
$y=\frac{12-3(-2)}{-4}$
$y=\frac{-12-6}{-4}$
$y=-\frac{-18}{-4}=4.5$
With the three points, $(2,-1.5), (0,3), (-2,4.5)$, 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.
