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!