Question

1. m = 3/2, b = -42.m = -3/2, b = 4determine how many solutions this can have.One ZeroInfinite

Answer 1

First let's write each equation using the slope-intercept form:

$y=mx+b$

So we have the following system:

$\begin{cases}y=\frac{3}{2}x-4 \\ y=-\frac{3}{2}x+4\end{cases}$

In order to solve this system, let's add both equation, this way we can find the value of y and then the value of x:

$\begin{gathered} y+y=\frac{3}{2}x-4+(-\frac{3}{2}x)+4 \\ 2y=0 \\ y=0 \\ \\ 0=\frac{3}{2}x-4 \\ \frac{3}{2}x=4 \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}$

So the solution to this system is (8/3, 0), therefore the system has one solution.