Question

7y+28=-3x and x+4y=-32 how many solutions does the system have?

Answer 1

The system of equations 7y+28=-3x and x+4y=-32 has a single solution, as the two lines are not parallel, which means they intersect at one point.

Step-by-step explanation:

To determine how many solutions the system of equations has, we need to analyze the two given equations: 7y+28=-3x and x+4y=-32.

First, let's rewrite the first equation in slope-intercept form (y=mx+b):

7y = -3x - 28
y = -x - 4

And the second equation:

x = -4y - 32
x = -4(y + 8)

Then, we check if the two lines are parallel, identical, or intersecting. As the coefficients of x and y are not multiples of each other, the lines are not parallel. Therefore, the system has a single solution, a point where the two lines intersect.