Answer
$(10,5)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$x-y=5$
$2x-3y=5$
Taking the first equation, we solve for y.
$x-y=5$
$-y=5-x$
$y=x-5$
Find three solutions:
For x=2,
$y=x-5$
$y=2-5$
$y=-3$
For x=0,
$y=x-5$
$y=0-5$
$y=-5$
For x=-2,
$y=x-5$
$y=-2-5$
$y=-7$
With the three points, $(2,-3), (0,-5), (-2,-7)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$2x-3y=5$
$-3y=5-2x$
$y=\frac{2x-5}{3}$
Find three solutions:
For x=2,
$y=\frac{2(2)-5}{3}$
$y=\frac{4-5}{3}$
$y=\frac{-1}{3}\approx-0.33$
For x=0,
$y=\frac{2(0)-5}{3}$
$y=\frac{0-5}{3}$
$y=\frac{-5}{3}\approx-1.67$
For x=-2,
$y=\frac{2(-2)-5}{3}$
$y=\frac{-4-5}{3}$
$y=\frac{-9}{3}\approx-3$
With the three points, $(2,-0.33), (0,-1.67), (-2,3)$, 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.
