Let us solve the given system of equations:

The system:

1. $4x - 3y = 10$
2. $5x + y = 22$

Step 1: Solve one equation for one variable

From equation (2): $y = 22 - 5x$

Step 2: Substitute $y$ into the first equation

Substitute $y = 22 - 5x$ into $4x - 3y = 10$: $4x - 3(22 - 5x) = 10$ Simplify: $4x - 66 + 15x = 10$ $19x - 66 = 10$ $19x = 76$ $x = 4$

Step 3: Substitute $x = 4$ into $y = 22 - 5x$

Substitute $x = 4$: $y = 22 - 5(4)$ $y = 22 - 20 = 2$

Final Answer:

The solution is: $x = 4, \, y = 2$

Select the correct choice:

This matches Option A: "The solution of the system is $x = 4$ and $y = 2$."

Would you like further clarification or details on the steps? Here are some related questions:

1. How do you verify the solution to a system of equations?
2. What methods exist to solve systems of equations (e.g., substitution, elimination)?
3. What does it mean if a system is inconsistent or has infinitely many solutions?
4. Can you graphically interpret this solution?
5. How can you set up systems of equations in word problems?

Tip: Always check your solution by substituting it into both original equations to confirm correctness!