Step 1

The equations are given by,

\(x-9y=-13\)...(1)

\(5x+3y=-15\)...(2)

Step 2

Multiply the equation (1) by 5 and subtract with equation (2) as follows.

\(5x-45y=-65\)

\(5x+3y=-15\)

\(-48y=-50\)

\(\displaystyle{y}={\frac{{{50}}}{{{48}}}}\)

\(\displaystyle{y}={\frac{{{25}}}{{{24}}}}\)

Substitute \(\displaystyle{y}={\frac{{{25}}}{{{24}}}}\) in equation (1).

\(\displaystyle{x}-{9}{\left({\frac{{{25}}}{{{24}}}}\right)}=-{13}\)

\(\displaystyle{x}-{\frac{{{225}}}{{{24}}}}=-{13}\)

\(\displaystyle{x}=-{13}+{\frac{{{225}}}{{{24}}}}\)

\(\displaystyle{x}=-{\frac{{{87}}}{{{24}}}}\)

\(\displaystyle{x}=-{\frac{{{29}}}{{{8}}}}\)

The solution of the system f equations are \(\displaystyle{x}=-{\frac{{{29}}}{{{8}}}},{y}={\frac{{{25}}}{{{24}}}}\).