The given equations are
y = 2x - 3
and
x + 3y = 12
We can make y the subject. It becomes
3y = 12 - x
y = 12/3 - x/3
y = 4 - x/3
We would substitute values of x into both equations to get corresponding values of y. These values would be plotted on the graph.
For the first equation,
if x = - 1, y = 2(-1) - 3 = - 2 - 3 = - 5
if x = 0, y = 2(0) - 3 = 0 - 3 = - 3
if x = 11, y = 2(11) - 3 = 2 - 3 = - 1
For the second equation,
If x = - 1, y = 4 - - 1/3 = 4 + 1/3 = 13/3
If x = 0, y = 4 - 0/3 = 4 + 0 = 4
If x = 1, y = 4 - 1/3 = 11/3
We would plot the x values on the horizontal axis and the corresponding y values on the vertical axis. The graph is shown below
The red line represents y = 2x - 3
The blue line represents y = 4 - x/3
The solution of the system of equations is the values of x and y at the point where both lines meet. Thus,the solutions are
x = 3
y = 3