https://file.aiquickdraw.com/mathbot/file/1725537186048ooon76v0.jpg

The system of equations provided in the image is:

\[
2x + 5y = 21
\]
\[
x + 2y = 7
\]

We need to solve for \(x\) and \(y\).

### Steps to solve:

1. From the second equation, express \(x\) in terms of \(y\):
   \[
   x = 7 - 2y
   \]

2. Substitute this expression for \(x\) in the first equation:
   \[
   2(7 - 2y) + 5y = 21
   \]

3. Simplify the equation:
   \[
   14 - 4y + 5y = 21
   \]
   \[
   14 + y = 21
   \]

4. Solve for \(y\):
   \[
   y = 21 - 14 = 7
   \]
   So, \(y = 7\).

5. Substitute \(y = 7\) into the equation \(x = 7 - 2y\):
   \[
   x = 7 - 2(7) = 7 - 14 = -7
   \]

Thus, the solution is \(x = -7\) and \(y = 7\).

Would you like more details on any of these steps?

### Relative Questions:
1. What is the substitution method for solving systems of equations?
2. How can the elimination method be used to solve this system?
3. How do we verify the solution for a system of equations?
4. What happens if a system of equations has no solutions?
5. How does solving linear systems graphically differ from algebraically?

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

Solve the system of equations 2x + 5y = 21 and x + 2y = 7 to find x and y.

Learn how to solve the system of linear equations 2x + 5y = 21 and x + 2y = 7 using the substitution method. This problem involves key algebraic concepts suitable for students in Grades 7-9. Follow a step-by-step solution to find x and y.

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