https://file.aiquickdraw.com/mathbot/file/1726959006980vid1gh03.jpg

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

\[
\begin{aligned}
5x - 2y &= 6 \\
10x + 2y &= 15
\end{aligned}
\]

### Step 1: Add the two equations
By adding both equations, we can eliminate the \( y \) term.

\[
(5x - 2y) + (10x + 2y) = 6 + 15
\]

This simplifies to:

\[
15x = 21
\]

### Step 2: Solve for \( x \)
Now, solve for \( x \):

\[
x = \frac{21}{15} = \frac{7}{5}
\]

### Step 3: Substitute \( x = \frac{7}{5} \) into one of the original equations
Substitute \( x = \frac{7}{5} \) into the first equation:

\[
5\left(\frac{7}{5}\right) - 2y = 6
\]

Simplifying:

\[
7 - 2y = 6
\]

Now, solve for \( y \):

\[
-2y = 6 - 7 = -1
\]

\[
y = \frac{1}{2}
\]

### Conclusion:
The solution is \( x = \frac{7}{5} \) and \( y = \frac{1}{2} \).

Thus, the correct option is **A**.

Let me know if you'd like further details or have questions.

### Related questions:
1. How can you determine if a system of equations is inconsistent?
2. What is the geometrical interpretation of an inconsistent system?
3. How would you solve the system if both equations were parallel?
4. What is the method of substitution, and how can it apply here?
5. How can you check your solution once you’ve solved a system of equations?

### Tip:
Always simplify the system or equations by eliminating one variable to make the solution easier.

Solve the system of equations: 5x - 2y = 6 and 10x + 2y = 15. If the system has no solution, say that it is inconsistent.

Learn how to solve the system of equations 5x - 2y = 6 and 10x + 2y = 15 using the method of elimination. This problem involves algebraic concepts such as solving simultaneous equations, and covers step-by-step solutions, including solving for x and y. Suitable for students in Grades 8-10.

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