Question

does the system of linear equations shown Below have one solution no solution or many solutions y = 3x - 2y = -2x + 3

Answer 1

Given the following system of equations:

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

if we equate both equations we get:

$3x-2=-2x+3$

then, if we solve for x, we get the following:

$\begin{gathered} 3x-2=-2x+3 \\ \Rightarrow3x+2x=3+2 \\ \Rightarrow5x=5 \\ x=1 \end{gathered}$

since we have that x = 1, this means that the system has one solution