The system of equations to be solved is given to be:
[tex]\begin{gathered} y=3x-5\text{ --------------\lparen1\rparen} \\ y=-6x+4\text{ --------------\lparen2\rparen} \end{gathered}[/tex]
Equate y in both equations to each other:
[tex]3x-5=-6x+4[/tex]
Solving, we have:
[tex]\begin{gathered} 3x+6x=4+5 \\ 9x=9 \\ x=1 \end{gathered}[/tex]
Put x = 1 into the first equation:
[tex]\begin{gathered} y=3(1)-5 \\ y=3-5 \\ y=-2 \end{gathered}[/tex]
Therefore, the solution to the system of equations is given to be:
[tex](x,y)=(1,-2)[/tex]
The graph is shown below:
