Solve a system of linear equations using augmented matrix Algebra II

Solve the following systems using augmented matrices.

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

x=\dfrac{3}{8} and y=\dfrac{3}{4}

x=\dfrac{11}{8} and y=\dfrac{-5}{4}

x=\dfrac{9}{4} and y=\dfrac{7}{6}

This system has no solution.

\begin{cases} 4x-2y=8 \cr \cr x+2y=6 \end{cases}

x=5 and y=15

x=10 and y=8

x=\dfrac{14}{5} and x=\dfrac{8}{5}

x=21 and y=6

\begin{cases} 2x-6y=12 \cr \cr 4x+6y=24 \end{cases}

x=9 and y=2

x=6 and y=0

x=10 and y=5

x=4 and y=4

\begin{cases} x-y=3 \cr \cr x+y=7 \end{cases}

x=4 and y=3

x=5 and y=2

x=9 and y=12

x=12 and y=9

\begin{cases} 5x-3y=12 \cr \cr -5x+y=10 \end{cases}

x=\dfrac{7}{2} and y=4

x=\dfrac{-17}{2} and y=-5

x=\dfrac{-21}{5} and y=-11

x=\dfrac{-13}{3} and y=-9

\begin{cases} x-2y=12 \cr \cr -x+y=8 \end{cases}

x=-28 and y=-20

x=12 and y=9

x=23 and y=14

x=7 and y=18

\begin{cases} 3x-4y=8 \cr \cr -3x+y=10 \end{cases}

x=\dfrac{-1}{3} and y=-21

x=\dfrac{-6}{5} and y=-12

x=\dfrac{-19}{2} and y=-3

x=\dfrac{-16}{3} and y=-6