https://file.aiquickdraw.com/mathbot/file/1725843131042r77wh86u.jpg

The image contains two equations:

\[
x + 7y = 4
\]
\[
2x - 3y = 2
\]

Let's solve this system of linear equations using the substitution or elimination method.

### Step 1: Solve for \(x\) from the first equation:
\[
x = 4 - 7y
\]

### Step 2: Substitute \(x = 4 - 7y\) into the second equation:
\[
2(4 - 7y) - 3y = 2
\]
Expanding:
\[
8 - 14y - 3y = 2
\]
Simplifying:
\[
8 - 17y = 2
\]
\[
-17y = 2 - 8
\]
\[
-17y = -6
\]
\[
y = \frac{-6}{-17} = \frac{6}{17}
\]

### Step 3: Substitute \(y = \frac{6}{17}\) back into the equation for \(x\):
\[
x = 4 - 7\left(\frac{6}{17}\right)
\]
\[
x = 4 - \frac{42}{17}
\]
\[
x = \frac{68}{17} - \frac{42}{17} = \frac{26}{17}
\]

Thus, the solution is:
\[
x = \frac{26}{17}, \quad y = \frac{6}{17}
\]

Let me know if you have any questions or need further clarification!

Here are 5 related questions:
1. How can you check if the solution is correct by substituting the values of \(x\) and \(y\) back into the original equations?
2. What are other methods for solving systems of linear equations besides substitution and elimination?
3. Can this system be solved using matrices or determinants (Cramer's rule)?
4. What happens when a system of equations has no solution or infinitely many solutions?
5. How would you solve the system graphically, and what would the graph look like?

**Tip:** Always verify the solution by plugging the values back into both original equations!

Solve the system of equations: x + 7y = 4, 2x - 3y = 2.

Learn how to solve the system of linear equations x + 7y = 4 and 2x - 3y = 2 using both substitution and elimination methods. This problem demonstrates key algebraic concepts and is suitable for students in Grades 9-11.

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