Solve the system using substitution. \( \left\{\begin{array}{l}-7 x-3 y=-45 \\ -5 x+y=-29\end{array}\right. \) One solution: No solution Infinite number of solutions \( > \) Next Question

Solve the system of equations \( -7x-3y=-45;-5x+y=-29 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-7x-3y=-45\\-5x+y=-29\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}-7x-3y=-45\\y=-29+5x\end{array}\right.\) - step2: Substitute the value of \(y:\) \(-7x-3\left(-29+5x\right)=-45\) - step3: Simplify: \(-22x+87=-45\) - step4: Move the constant to the right side: \(-22x=-45-87\) - step5: Subtract the numbers: \(-22x=-132\) - step6: Change the signs: \(22x=132\) - step7: Divide both sides: \(\frac{22x}{22}=\frac{132}{22}\) - step8: Divide the numbers: \(x=6\) - step9: Substitute the value of \(x:\) \(y=-29+5\times 6\) - step10: Calculate: \(y=1\) - step11: Calculate: \(\left\{ \begin{array}{l}x=6\\y=1\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=6\\y=1\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(6,1\right)\) The system of equations has a unique solution, which is \( x = 6 \) and \( y = 1 \).