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
x
y
y=4/3x+4
y=-1/2x
To solve the system of equations graphed on the coordinate axes, we need to find the point(s) where the two equations intersect.
First, let's set the two equations equal to each other since they both equal y:
4/3x + 4 = -1/2x - 7
To simplify the equation, let's get rid of the fractions by multiplying everything by 6:
6 * (4/3x + 4) = 6 * (-1/2x - 7)
8x + 24 = -3x - 42
Now, let's move all the x terms to one side and all the constant terms to the other side:
8x + 3x = -42 - 24
11x = -66
Dividing both sides by 11, we find:
x = -6
Now, let's substitute this value of x back into one of the equations to solve for y:
y = 4/3x + 4
y = 4/3(-6) + 4
y = -8 + 4
y = -4
Therefore, the solution to the system of equations is (-6, -4).
The point of intersection of the two lines is (-6, -4).