Solve the system of equations graphed on the coordinate axes below.
y, equals, start fraction, 4, divided by, 3, end fraction, x, plus, 4
y=
3
4
x+4
y, equals, minus, one half, x, minus, 7
y=
−
2
1
x−7
To solve the system of equations, we need to find the intersection point of the two lines on the coordinate axes.
Looking at the graph, it appears that the two lines intersect at the point (2, 1).
To confirm this, we can substitute the x-coordinate (2) into both equations and solve for y:
For the first equation:
y = (4/3)x + 4
y = (4/3)(2) + 4
y = (8/3) + 12/3
y = 20/3
For the second equation:
y = -1/2x - 7
y = (-1/2)(2) - 7
y = -1 - 7
y = -8
Therefore, the two lines intersect at the point (2, 1).