**Solve this 2 system equations 2x - y = 7 and 6x - 3y = 14**

Let's solve the system of equations:

\[
\begin{align*}
1. & \quad 2x - y = 7 \\
2. & \quad 6x - 3y = 14
\end{align*}
\]

### Step-by-Step Solution

**Step 1: Simplify the equations if possible.**

Let's simplify the second equation:

\[
6x - 3y = 14
\]

Divide the entire equation by 2:

\[
3x - \frac{3}{2}y = 7
\]

Simplify by dividing all terms by 3:

\[
x - \frac{y}{2} = \frac{7}{3}
\]

Multiply by 2 to clear the fraction:

\[
2x - y = \frac{14}{3}
\]

Now let's check if both equations are identical. To do this, let's multiply the first equation by 3:

\[
3(2x - y) = 3 \cdot 7
\]

This gives:

\[
6x - 3y = 21
\]

Compare this with the second equation:

\[
6x - 3y = 14
\]

The equations are not consistent, meaning they do not match. They actually contradict each other after multiplying the first equation by 3.

### Conclusion

The system of equations:

\[
\begin{align*}
2x - y &= 7 \\
6x - 3y &= 14
\end{align*}
\]

is inconsistent. This means that there is **no solution** to this system because these two lines are parallel and do not intersect.

Would you like further details or have any questions?

### Relative Questions

1. What does it mean for two lines to be parallel in the context of linear equations?
2. How can we determine if a system of equations has exactly one solution?
3. What are other methods to solve systems of equations besides elimination?
4. How can you solve a system of equations using matrix methods?
5. How does the slope of a line relate to the solutions of a system of equations?

**Tip:** Always check if two equations are proportional to determine if they might be parallel or represent the same line.

Learn how to solve the system of equations 2x - y = 7 and 6x - 3y = 14 with a detailed step-by-step solution. This problem involves understanding linear equations and determining consistency in systems of equations. Suitable for students in Grades 8-10.

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