The solution to the system of equation 4x - y = -2 and x - y = 1 is x = -1 and y = -2.
Given the system of equations in the question:
4x - y = -2
x - y = 1
To solve the system of equations by graphing, we simply plot the line of each equation on the same set of axes and find the point where they intersect.
First, rearrange the equations in slope-intercept form:
y = 4x + 2
y = x - 1
Plotting the first equations:
Slope m = 4
x-intercept:
0 = 4x + 2
4x = -2
x = -2/4 = -1/2
(-1/2, 0)
y-intercept:
y = 4(0) + 2
y = 2
(0,2)
Plotting the second equation:
Slope = 1
x-intercept:
0 = x - 1
x = 1
(1,0)
y-intercept:
y = x - 1
y = 0 - 1
y = 1
(0,1)
Now, from the graph, the point of intersection of the two equations is (-1,-2).
Therefore, the solution is x = -1 and y = -2.