Answer
$(3,5)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$5x-y=10$
$x-3y=-12$
Taking the first equation, we solve for y.
$5x-y=10$
$-y=10-5x$
$y=5x-10$
Find three solutions:
For $x=2$,
$y=5(2)-10$
$y=10-10$
$y=0$
For $x=0$,
$y=5(0)-10$
$y=0-10$
$y=-10$
For $x=-2$,
$y=5(-2)-10$
$y=-10-10$
$y=-20$
With the three points, $(2,0), (0,-10), (-2,-20)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$x-3y=-12$
$-3y=-12-x$
$y=\frac{-12-x}{-3}$
Find three solutions:
For $x=2$,
$y=\frac{-12-2}{-3}$
$y=\frac{-12-2}{-3}$
$y=-\frac{-14}{-3}\approx4.7$
For $x=0$,
$y=\frac{-12-0}{-3}$
$y=\frac{-12}{-3}$
$y=4$
For $x=-2$,
$y=\frac{-12-(-2)}{-3}$
$y=\frac{-12+2}{-3}$
$y=-\frac{-10}{-3}\approx3.3$
With the three points, $(2,4.7), (0,4), (-2,3.3)$, 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.
