Answer
$(0.5,-3)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$4x-3y=11$
$6x+5y=-12$
Taking the first equation, we solve for y.
$4x-3y=11$
$-3y=11-4x$
$y=\frac{11-4x}{-3}$
$y=\frac{4x-11}{3}$
Find three solutions:
For x=2,
$y=\frac{4(2)-11}{3}$
$y=\frac{8-11}{3}$
$y=-1$
For x=0,
$y=\frac{4(0)-11}{3}$
$y=\frac{-11}{3}$
$y=-\frac{11}{3}\approx-3.7$
For x=-2,
$y=\frac{4(-2)-11}{3}$
$y=\frac{-8-11}{3}$
$y=-\frac{19}{3}\approx-6.3$
With the three points: (2,-1), (0,-3.7) y (-2,-6.3) we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$6x+5y=-12$
$5y=-12-6x$
$y=\frac{-12-6x}{5}$
Find three solutions:
For x=2,
$y=\frac{-12-6(2)}{5}$
$y=\frac{-12-12}{5}$
$y=-\frac{24}{5}\approx-4.8$
For x=0,
$y=\frac{-12-6(0)}{5}$
$y=\frac{-12}{5}$
$y=-\frac{12}{5}\approx-2.4$
For x=-2,
$y=\frac{-12-6(-2)}{5}$
$y=\frac{-12+12}{5}$
$y=-\frac{0}{5}=0$
With the three points: (2,-4.8), (0,-2.4) y (-2,0), we can graph the straight line that goes through these points.
The intersection point between this two lines is the answer to the system of equations.
