9) \( \begin{array}{l}5 x+y=9 \\ 10 x-7 y=-18\end{array} \)

Solve the system of equations \( 5x+y=9;10x-7y=-18 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5x+y=9\\10x-7y=-18\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=9-5x\\10x-7y=-18\end{array}\right.\) - step2: Substitute the value of \(y:\) \(10x-7\left(9-5x\right)=-18\) - step3: Simplify: \(45x-63=-18\) - step4: Move the constant to the right side: \(45x=-18+63\) - step5: Add the numbers: \(45x=45\) - step6: Divide both sides: \(\frac{45x}{45}=\frac{45}{45}\) - step7: Divide the numbers: \(x=1\) - step8: Substitute the value of \(x:\) \(y=9-5\times 1\) - step9: Substitute back: \(y=9-5\) - step10: Calculate: \(y=4\) - step11: Calculate: \(\left\{ \begin{array}{l}x=1\\y=4\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=4\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(1,4\right)\) The solution to the system of equations is \( x = 1 \) and \( y = 4 \).