Answer
$(-2,1)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$3x+y=-5$
$2x+5y=1$
Taking the first equation, we solve for y.
$3x+y=-5$
$y=-5-3x$
Find three solutions:
For x=2,
$y=-5-3x$
$y=-5-3(2)$
$y=-5-6=-11$
For x=0,
$y=-5-3x$
$y=-5-3(0)$
$y=-5-0=-5$
For x=-2,
$y=-5-3x$
$y=-5-3(-2)$
$y=-5+6=1$
With the three points: (2,-11), (0,-5) y (-2,1) we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$2x+5y=1$
$5y=1-2x$
$y=\frac{1-2x}{5}$
Find three solutions:
For x=2,
$y=\frac{1-2(2)}{5}$
$y=\frac{1-4}{5}$
$y=\frac{-3}{5}=-0.6$
For x=0,
$y=\frac{1-2(0)}{5}$
$y=\frac{1}{5}$
$y=\frac{1}{5}=0.2$
For x=-2,
$y=\frac{1-2(-2)}{5}$
$y=\frac{1+4}{5}$
$y=-\frac{5}{5}=1$
With the three points, $(2,-0.6), (0,0.2), (-2,1)$, 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.
