Answer
$(4,-1)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$2x-y=9$
$-2x+3y=-11$
Taking the first equation, we solve for y.
$2x-y=9$
$-y=9-2x$
$y=2x-9$
Find three solutions:
For x=2,
$y=2x-9$
$y=2(2)-9$
$y=4-9=-5$
For x=0,
$y=2x-9$
$y=2(0)-9$
$y=0-9=-9$
For x=-2,
$y=2x-9$
$y=2(-2)-9$
$y=-4-9=-13$
With the three points, $(2,-5), (0,-9), (-2,-13)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$-2x+3y=-11$
$3y=-11+2x$
$y=\frac{2x-11}{3}$
Find three solutions:
For x=2,
$y=\frac{2(2)-11}{3}$
$y=\frac{4-11}{3}$
$y=\frac{-7}{3}\approx-2.33$
For x=0,
$y=\frac{2(0)-11}{3}$
$y=\frac{0-11}{3}$
$y=\frac{-11}{3}\approx-3.67$
For x=-2,
$y=\frac{2(-2)-11}{3}$
$y=\frac{-4-11}{3}$
$y=\frac{-15}{3}\approx-5$
With the three points, $(2,-2.33), (0,-3.67), (-2,-5)$, 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.
