[tex]x=-6, y=5[/tex]
1) Let's solve this system of equations, by using the Elimination Method so, let's begin by multiplying by (-4) and (5) respectively so we can eliminate the x-terms when adding both equations simultaneously:
[tex]\begin{gathered} 5x+6y=0 \\ 4x-5y=-49 \\ \\ 5x+6y=0\:\times(-4) \\ 4x-5y=-49\:\times(5) \\ \\ -20x-24y=0 \\ 20x-25y=-245 \\ --------- \\ -49y=-245 \\ \\ \frac{-49y}{-49}=\frac{-245}{-49} \\ \\ y=5 \end{gathered}[/tex]
2) Now, let's plug y=5 into any original equation to solve for x:
[tex]\begin{gathered} 5x+6(5)=0 \\ \\ 5x+30=0 \\ \\ 5x+30-30=-30 \\ \\ 5x=-30 \\ \\ \frac{5x}{5}=-\frac{30}{5} \\ \\ x=-6 \end{gathered}[/tex]
3) Hence, the answer is:
[tex]x=-6,\:y=5[/tex]
