X7+2Y = 10 (Right answers are X=2, Y = -2)

X7 + 2Y = 10

X + Y = 7 + 2 = 9

X = 9 - 7 = 2
Y = -X

X7 + 2Y = 2*7 + 2 * -2 = 10

Check I'm right and don't broke any math rules?

Let's break down the given equations and check the correctness of your solution.

### Given Equations:
1. \( X7 + 2Y = 10 \)  
2. \( X + Y = 9 \)  

### Steps:
1. **Understanding the first equation:**
   - The expression \( X7 \) typically means \( 7X \), so we rewrite the equation as:
   \[
   7X + 2Y = 10
   \]
   
2. **From the second equation:**
   \[
   X + Y = 9
   \]
   
3. **Solving the second equation for \( Y \):**
   \[
   Y = 9 - X
   \]

4. **Substituting \( Y = 9 - X \) into the first equation:**
   \[
   7X + 2(9 - X) = 10
   \]
   \[
   7X + 18 - 2X = 10
   \]
   \[
   5X + 18 = 10
   \]
   \[
   5X = 10 - 18
   \]
   \[
   5X = -8
   \]
   \[
   X = -\frac{8}{5}
   \]

This shows that \( X = 2 \) is not correct. 

5. **Finding \( Y \) using the correct \( X \):**
   \[
   Y = 9 - \left(-\frac{8}{5}\right) = \frac{45}{5} + \frac{8}{5} = \frac{53}{5}
   \]

### Conclusion:
The correct solution is \( X = -\frac{8}{5} \) and \( Y = \frac{53}{5} \). 

### Check:
Substitute \( X = -\frac{8}{5} \) and \( Y = \frac{53}{5} \) into the original equation:
\[
7\left(-\frac{8}{5}\right) + 2\left(\frac{53}{5}\right) = -\frac{56}{5} + \frac{106}{5} = \frac{50}{5} = 10
\]
This matches, confirming the correct values.

Your initial assumption was incorrect as the right solution doesn't satisfy the original equations.

Would you like a deeper explanation of these steps or have other questions?

### Follow-up Questions:
1. Can you solve for \( Y \) if given only the first equation?
2. How would you solve it if the equations were non-linear?
3. What would happen if the constant term on the right side was different?
4. How can you solve a system of equations using substitution vs elimination?
5. What if the coefficient of \( X \) wasn't 7 but another number?

### Tip:
Always verify your solution by substituting the values back into the original equations.

Explore how to solve linear equations using the substitution method with a step-by-step explanation. This problem involves substituting variables and simplifying equations, suitable for students in Grades 7-9.

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