The given system of equations is expressed as
Y=-1/2x-1
Y=1/4x-4
We would assume values for x and substitute them into the equations to get corresponding values for y. We would plot these x and y values on the graph. The x and y values corresponding to the point where the two lines meet represents the solution of the system of equations.
For the first equation,
If x = 0, y = - 1/2*0 - 1 = - 1
If x = 1, y = - 1/2 * 1 - 1 = - 3/2
If x = 2, y = - 1/2 * 2 - 1 = - 2
For the second equation,
if x = 0, y = 1/4*0 - 4 = - 4
If x = 1, y = 1/4*1 - 4 = - 15/4
If x = 2, y = 1/4*2 - 4 = - 7/2
The graph is shown below
Looking at the graph, the red line represents y = - x/2 - 1 while the blue line represents
y = x/4 - 4
At the point where both lines meet,
x = 4, y = - 3
Thus, the solution of the system of equations is (4, - 3)