Answer
$(2,-2)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$4x+3y=2$
$5x-y=12$
Taking the first equation, we solve for y.
$4x+3y=2$
$3y=2-4x$
$y=\frac{2-4x}{3}$
Find three solutions:
For x=2,
$y=\frac{2-4(2)}{3}$
$y=\frac{2-8}{3}$
$y=\frac{-6}{3}=-2$
For x=0,
$y=\frac{2-4(0)}{3}$
$y=\frac{2-0}{3}$
$y=\frac{2}{3}\approx0.67$
For x=-2,
$y=\frac{2-4(-2)}{3}$
$y=\frac{2+8}{3}$
$y=\frac{10}{3}\approx3.3$
With the three points: (2,-2), (0,0.67) y (-2,3.3) we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$5x-y=12$
$-y=12-5x$
$y=5x-12$
Find three solutions:
For x=2,
$y=5x-12$
$y=5(2)-12$
$y=10-12=-2$
For x=0,
$y=5x-12$
$y=5(0)-12$
$y=0-12=-12$
For x=-2,
$y=5x-12$
$y=5(-2)-12$
$y=-10-12=-22$
With the three points, $(2,-2), (0,-12), (-2,-22)$, 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.
