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The given system of equations had a solution(x,y) what is the value of x?

Let's solve the system of equations provided in the image:

The system is:

\[
\begin{aligned}
3x + y &= 3 \\
7x - y &= 2
\end{aligned}
\]

We can solve this by elimination or substitution. I'll use the elimination method:

1. Add the two equations together to eliminate \(y\):
\[
(3x + y) + (7x - y) = 3 + 2
\]
Simplifying:
\[
10x = 5
\]
So,
\[
x = \frac{5}{10} = 0.5
\]

Thus, the value of \(x\) is \(0.5\).

Would you like to solve for \(y\) as well, or need more clarification?

### Follow-up questions:
1. What is the value of \(y\) using this solution?
2. How would the solution change if the second equation had a different constant?
3. Can you solve the same system using substitution instead of elimination?
4. What does it mean geometrically to solve a system of linear equations?
5. How do we determine if a system of linear equations has no solution or infinitely many solutions?

**Tip**: Always double-check your work by substituting the solution back into the original equations!

The given system of equations has a solution (x, y). What is the value of x?

Learn how to solve the system of linear equations 3x + y = 3 and 7x - y = 2 using the elimination method. This problem is suitable for students in Grades 8-10 and covers key algebraic techniques for solving systems of equations.

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