Let's solve this step by step:

Problem:

1. Sum of two numbers: $x + y = 11$ (where $x$ is the greater number and $y$ is the lesser).
2. Twice the greater number minus the lesser number equals 7: $2x - y = 7$.

We need to find the greater number, $x$.

Solving the System of Equations:

1. Express $y$ from the first equation:

$y = 11 - x$

2. Substitute $y = 11 - x$ into the second equation:

$2x - (11 - x) = 7$

3. Simplify:

$2x - 11 + x = 7$ $3x - 11 = 7$

4. Solve for $x$:

$3x = 18$ $x = 6$

Greater Number:

The greater number is 6.

Would you like me to explain further or assist with another question?
Here are some related practice questions:

1. What is the lesser number in this problem?
2. Can you solve another system of equations with different sums and differences?
3. If the sum of two numbers is 15 and twice the lesser number minus the greater is 1, what is the greater number?
4. What are some real-world scenarios where this type of equation could apply?
5. How would the solution change if the sum was $12$ and $2x - y = 10$?

Tip: Always start by simplifying one equation to express one variable in terms of the other!