Solve the system by any method. \( \begin{array}{r}x+4 y=5 \\ 2 x+5 y=4 \\ 3 x+6 y=3 \\ 4 x+7 y=2\end{array} \) Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The solution to the system is \( \square \). (Type an ordered pair.) B. This system has infinitely many solutions of the form ( \( \square, y) \), where \( y \) is any real number. (Type an expression using \( y \) as the variable.) C. The system has no solution.

Solve the system of equations \( x+4y=5;2x+5y=4;3x+6y=3;4x+7y=2 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+4y=5\\2x+5y=4\\3x+6y=3\\4x+7y=2\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=5-4y\\2x+5y=4\\3x+6y=3\\4x+7y=2\end{array}\right.\) - step2: Substitute the value of \(x:\) \(\left\{ \begin{array}{l}2\left(5-4y\right)+5y=4\\3\left(5-4y\right)+6y=3\\4\left(5-4y\right)+7y=2\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}10-3y=4\\15-6y=3\\20-9y=2\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}y=2\\15-6y=3\\20-9y=2\end{array}\right.\) - step5: Substitute the value of \(y:\) \(\left\{ \begin{array}{l}15-6\times 2=3\\20-9\times 2=2\end{array}\right.\) - step6: Simplify: \(\left\{ \begin{array}{l}3=3\\2=2\end{array}\right.\) - step7: Substitute the value of \(y:\) \(x=5-4\times 2\) - step8: Simplify: \(x=-3\) - step9: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=2\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=2\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(-3,2\right)\) The solution to the system of equations is \( (x, y) = (-3, 2) \). Therefore, the correct answer is: A. The solution to the system is (-3, 2).