Solve the system of equations graphed on the coordinate axes below.
y, equals, one half, x, plus, 8
y=
2
1
x+8
y, equals, minus, 4, x, plus, 8
y=
−4x+8
x
y
y=1/2x+8
y=-4x+8
The system of equations can be solved by finding the point of intersection between the two graphs.
To find the intersection point, we can set the two equations equal to each other and solve for x:
1/2x + 8 = -4x + 8
Adding 4x to both sides:
4.5x + 8 = 8
Subtracting 8 from both sides:
4.5x = 0
Dividing both sides by 4.5:
x = 0
Now we can substitute this value of x back into either of the original equations to find the corresponding y-value. Let's use the equation y = 1/2x + 8:
y = 1/2(0) + 8
y = 0 + 8
y = 8
Therefore, the intersection point of the two graphs is (0, 8).