Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, one half, x, plus, 6
y=
−
2
1
x+6
y, equals, start fraction, 3, divided by, 2, end fraction, x, minus, 2
y=
2
3
x−2
To solve the system of equations, we need to find the values of x and y that satisfy both equations.
Looking at the graphs, we can see that the two lines intersect at a point. This point is the solution to the system of equations.
To find the coordinates of the intersection point, we can set the two equations equal to each other:
-1/2x + 6 = 3/2x - 2
By combining like terms and simplifying, we get:
4x = 16
Dividing both sides by 4, we find:
x = 4
Now, we can substitute this value of x into one of the original equations to find y:
y = -1/2(4) + 6
y = -2 + 6
y = 4
Therefore, the solution to the system of equations is (4, 4).