Part A:The first equation is:
[tex]\begin{gathered} y=\frac{2}{3}x-1 \\ 3y=2x-3 \\ -2x+3y=-3 \end{gathered}[/tex]
Which is the same as the second equation.
Hence the system has infinitely mant solutions.
Part B:The equations are:
[tex]y=-\frac{1}{2}x-\frac{3}{2},y=-2x-6[/tex]
Solve the equations to get:
[tex]\begin{gathered} \frac{-1}{2}x-\frac{3}{2}=-2x-6 \\ \frac{3}{2}x=\frac{-9}{2} \\ x=-3 \end{gathered}[/tex]
Substitute the value of x in any of the equations to get:
[tex]y=\frac{-1}{2}\times-3-\frac{3}{2}=0[/tex]
Hence the system has unique solution whicch is (-3,0)
Part C:The equations are:
[tex]y=\frac{2}{3}x-2,y=\frac{2}{3}x-3[/tex]
The system represents a pair of parallel lines hence the system has no solution:
