Questions: When solving systems of equations, you can check your answer by: Substituting the values of the variables into the first equation and then simplifying to make sure that you get a true statement. Substituting the values of the variables into the second equation and then simplifying to make sure you get a true statement. Substituting the values of the variables into both equations and then simplifying to make sure that you get two true statements.

Solution Steps

To check the solution of a system of equations, you need to substitute the values of the variables into each equation and verify that both equations hold true.

We are given the system of equations: \[ \begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases} \]

We substitute \( x = 2 \) and \( y = 3 \) into the first equation: \[ 2 + 3 = 5 \] This simplifies to: \[ 5 = 5 \] which is a true statement.

Next, we substitute \( x = 2 \) and \( y = 3 \) into the second equation: \[ 2(2) - 3 = 1 \] This simplifies to: \[ 4 - 3 = 1 \] which is also a true statement.

Final Answer