Solve the system by graphing. Check your solution
y=-x+1
y=x-7
To solve the system by graphing, we will graph both equations on the same coordinate plane and find the point of intersection.
For the first equation, y = -x + 1, we can plot a few points to make a straight line:
x = 0, y = -0 + 1 = 1
x = 1, y = -1 + 1 = 0
x = -1, y = 1 - 1 = 0
Plotting these points, we can draw a line that passes through them:
For the second equation, y = x - 7, we can also plot a few points:
x = 0, y = 0 - 7 = -7
x = 1, y = 1 - 7 = -6
x = -1, y = -1 - 7 = -8
Plotting these points, we can draw another line:
The two lines intersect at the point (4, -3). This is the solution to the system of equations.
To check our solution, we substitute the x and y values into both equations:
For y = -x + 1:
-3 = -4 + 1
-3 = -3
For y = x - 7:
-3 = 4 - 7
-3 = -3
Both equations are satisfied with the values x = 4 and y = -3, so our solution is correct.