You have the following system of equations:
5x + 2y = 4
3x + 6y = -12
In order to solve the previous equation by graphing, first, solve each equation for y, just as follow:
5x + 2y = 4
2y = -5x + 4
y = -5/2 x + 2
3x + 6y = -12
6y = -3x - 12
y = -1/2 x - 2
To graph each equation calculate both x and y intercepts. TO calculate x intercepts, equal y = 0 and solve for x:
0 = -5/2 x + 2
-2 = -5/2x
-4 = -5x
4/5 = x
0 = -1/2 x - 2
1/2x = -2
x = -4
For the y-intercept, only evaluate each equation for x=0:
y = -5/2 (0) + 2
y = 2
y = -1/2 (0) - 2
y = - 2
Hence, the x and y intercepts are:
(4/5 , 0) and (0 , 2) for the first equation of the system
(-4 , 0) and (0 , -2) for the second equation of the system
Then, the graphs of the equations are:
In the previous graph you can notice the x and y intercepts of each line, also you can notice that the lines intercept each other on th point (2,-3).
Hence, the solution to the given system of equations is:
x = 2
y = -3