It is required to solve the following system of equations by graphing:
[tex]\begin{cases}y={x+3} \\ 12x+y=-6{}\end{cases}[/tex]
To do this, graph each line on the same coordinate plane, and find the point of intersection of the lines.
Graph the first line, y=x+3:
Find two points that satisfy the equation of the line.
Substitute x=0 into the first equation and find the value of y:
[tex]y=0+3=3[/tex]
Hence, the line passes through the point (0,3).
Substitute x=-2 into the first equation and find the value of y to get a second point:
[tex]y=-2+3=1[/tex]
Hence, the line also passes through the point (-2,1).
Plot the points on the coordinate plane and join them with a straight line as shown below:
Next, graph the second line using the same procedure as the first:
Locate the point of intersection:
The point of intersection is (-3,0).
Hence, the solution to the system of equations is (x,y)=(-3,0), that is, x=-3, y=0.
The solution is x=-3 and y=0.
