Solving for x in the second equation, we get:
[tex]\begin{gathered} -3x+4y=-13 \\ -3x=-13-4y \\ x=\frac{-13}{-3}-\frac{4y}{(-3)} \\ x=\frac{13}{3}+\frac{4y}{3} \end{gathered}[/tex]
Replacing x on the first one and solving for y, we get:
[tex]\begin{gathered} 2x+5y=1 \\ 2(\frac{13}{3}+\frac{4y}{3})+5y=1 \\ \frac{26}{3}+\frac{8y}{3}+5y=1 \\ \frac{8y}{3}+5y=1-\frac{26}{3} \\ \frac{23}{3}y=\frac{-23}{3} \\ y=-1 \end{gathered}[/tex]
Finally, replacing y by -1, we get:
[tex]\begin{gathered} x=\frac{13}{3}+\frac{4}{3}\cdot(-1) \\ x=\frac{13}{3}-\frac{4}{3} \\ x=3 \end{gathered}[/tex]
Answer: x = 3 and y = -1
