We have the following system of equations:
[tex]\begin{gathered} 4x+8y=4 \\ -2x-7y=-11\ldots(A) \end{gathered}[/tex]
Solving by combining equations:
If we multiply equation A by 2, we get the following equivalent system:
[tex]\begin{gathered} \\ 4x+8y=4\ldots(B) \\ -4x-14y=-22\ldots(C) \end{gathered}[/tex]
If we add both equation, we have
[tex]8y-14y=4-22[/tex]
which gives
[tex]-6y=-18[/tex]
If we move the coefficient of y, we get
[tex]\begin{gathered} y=\frac{-18}{-6} \\ y=3 \end{gathered}[/tex]
Finally, by substituting this result into equation B, we obtain
[tex]4x+8(3)=4[/tex]
which leads to
[tex]4x+24=4[/tex]
If we move +24 to the right hand side,we get
[tex]\begin{gathered} 4x=4-24 \\ 4x=-20 \end{gathered}[/tex]
and x is given by
[tex]\begin{gathered} x=\frac{-20}{4} \\ x=-5 \end{gathered}[/tex]
Therefore, the answer is
[tex]\begin{gathered} x=-5 \\ y=3 \end{gathered}[/tex]
