Determine whether the given ordered pair is a solution of the system.
​(5​,2​)
xminusyequals3
xplusyequals8
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Part 1
Is the ordered pair a solution of the​ system?

To determine whether the given ordered pair \((5, 2)\) is a solution of the system of equations:

1. \(x - y = 3\)
2. \(x + y = 8\)

we need to substitute \(x = 5\) and \(y = 2\) into both equations and check if they hold true.

### Substitution into the First Equation

Substitute \(x = 5\) and \(y = 2\) into the first equation:
\[ x - y = 3 \]

\[ 5 - 2 = 3 \]
\[ 3 = 3 \]

This equation holds true.

### Substitution into the Second Equation

Substitute \(x = 5\) and \(y = 2\) into the second equation:
\[ x + y = 8 \]

\[ 5 + 2 = 8 \]
\[ 7 = 8 \]

This equation does not hold true.

Since the ordered pair \((5, 2)\) satisfies the first equation but does not satisfy the second equation, it is not a solution to the system of equations.

### Conclusion
The ordered pair \((5, 2)\) is **not** a solution of the system.

Would you like more details or have any questions?

Here are 5 questions you might want to ask next:
1. Can you explain how to solve a system of equations using substitution?
2. How do you solve a system of equations using elimination?
3. What are the different methods for solving systems of equations?
4. Can you provide another example of solving a system of equations?
5. How can we graphically interpret the solution of a system of equations?

**Tip:** When solving systems of equations, always substitute the values back into the original equations to verify if they satisfy both equations.

Check if the ordered pair (5, 2) is a solution to the system of equations x - y = 3 and x + y = 8. Understand the application of the substitution method in solving systems of linear equations.

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