Given the equations:
[tex]\begin{gathered} x-4y=-11 \\ 2x+y=23 \end{gathered}[/tex]
For the first equation:
[tex]\begin{gathered} x-4y+4y=-11+4y \\ x=-11+4y \end{gathered}[/tex]
Substitute x in the second equation:
[tex]2(-11+4y)+y=23[/tex]
Simplify:
[tex]\begin{gathered} -22+8y+y=23 \\ -22+9y=23 \end{gathered}[/tex]
Solve for y:
[tex]\begin{gathered} -22+9y+22=23+22 \\ 9y=45 \\ \frac{9y}{9}=\frac{45}{9} \\ y=5 \end{gathered}[/tex]
Then, substitute y = 5 in x:
[tex]x=-11+4(5)=-11+20=9[/tex]
Answer:
x = 9
y = 5
