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.

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.
Transcript text: 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.
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Solution

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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.

Step 1: Define the System of Equations

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

Step 2: Substitute the Solution into the First Equation

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

Step 3: Substitute the Solution into the Second Equation

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

\(\boxed{x = 2, y = 3}\)

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