The given system of equations is:
[tex]\begin{gathered} y=6x-11\text{ Eq.(1)} \\ -2x-3y=-7\text{ Eq.(2)} \end{gathered}[/tex]We can start by substituting Eq 1 into Eq 2 and solve for x:
[tex]-2x-3(6x-11)=-7[/tex]Apply the distributive property:
[tex]\begin{gathered} -2x-3\times6x+3\times11=-7 \\ -2x-18x+33=-7 \\ -20x+33=-7 \\ -20x=-7-33 \\ -20x=-40 \\ x=\frac{-40}{-20} \\ x=2 \end{gathered}[/tex]Now, replace the x-value into equation 1 and solve for y:
[tex]\begin{gathered} y=6(2)-11 \\ y=12-11 \\ y=1 \end{gathered}[/tex]Answer: x=2 and y=1
