The sum of two numbers is 35 and their difference is 5 . What are the two numbers? Let \( x= \) one number and \( y= \) the other number. The corresponding modeling system is \( \left\{\begin{array}{l}x+y=35 \\ x-y=5\end{array}\right. \). Solve the system graphically.

Solve the system of equations \( x+y=35;x-y=5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=35\\x-y=5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=35-y\\x-y=5\end{array}\right.\) - step2: Substitute the value of \(x:\) \(35-y-y=5\) - step3: Subtract the terms: \(35-2y=5\) - step4: Move the constant to the right side: \(-2y=5-35\) - step5: Subtract the numbers: \(-2y=-30\) - step6: Change the signs: \(2y=30\) - step7: Divide both sides: \(\frac{2y}{2}=\frac{30}{2}\) - step8: Divide the numbers: \(y=15\) - step9: Substitute the value of \(y:\) \(x=35-15\) - step10: Simplify: \(x=20\) - step11: Calculate: \(\left\{ \begin{array}{l}x=20\\y=15\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=20\\y=15\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(20,15\right)\) The solution to the system of equations \(x+y=35\) and \(x-y=5\) is \(x=20\) and \(y=15\). Therefore, the two numbers are 20 and 15.