Question

how many solutions has the following system explained by analyzing the slope and the y-intercept mean y = 3/2 x - 13y = x + 2

Answer 1

Given the system of equations :

$\begin{gathered} y=\frac{3}{2}x-1 \\ 3y=x+2 \end{gathered}$

We will write the equations in slope - intercept form : y = m * x + b

So, the equations will be :

$\begin{gathered} y=\frac{3}{2}x-1\rightarrow(1) \\ \\ y=\frac{1}{3}x+\frac{2}{3}\rightarrow(2) \end{gathered}$

For the equation (1)

The slope = 3/2 , and y- intercept = -1

For the equation (2):

The slope = 1/3 , and y- intercept = 2/3

As we can , the slopes of the lines are different and so the y- intercepts

So, there is only one solution fro the given system of equations.