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.