first solve each equation for y
[tex]\begin{gathered} 2x-9y=-5 \\ -9y=-5-2x \\ y=\frac{5}{9}+\frac{2}{9}x \end{gathered}[/tex][tex]\begin{gathered} 4x-y=2 \\ -y=2-4x \\ y=-2+4x \end{gathered}[/tex]the equations are
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \end{gathered}[/tex]we can substract the equations to remove y
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \\ \\ ---------------- \\ 0=\frac{23}{9}-\frac{34}{9}x \end{gathered}[/tex]now solve x
[tex]\begin{gathered} \frac{23}{9}-\frac{34}{9}x=0 \\ \\ 23-34x=0 \\ 34x=23 \\ \\ x=\frac{23}{34} \end{gathered}[/tex]the value of x is 23/34, now replace on any equation to find Y, I will replace on the second
[tex]\begin{gathered} y=-2+4(\frac{23}{34}) \\ \\ y=-2+\frac{46}{17} \\ \\ y=\frac{12}{17} \end{gathered}[/tex]the value of y is 12/17
the solution point is ( 23/34 , 12/17)