To solve the given system of equations using the substitution method:

1. The system of equations is: x - y = 1 \tag{1} 4x + 3y = 25 \tag{2}

Step 1: Solve one equation for one variable

From equation (1), solve for $x$ in terms of $y$: x = y + 1 \tag{3}

Step 2: Substitute into the other equation

Substitute $x = y + 1$ from equation (3) into equation (2): $4(y + 1) + 3y = 25$ Simplify: $4y + 4 + 3y = 25$ $7y + 4 = 25$ $7y = 21$ $y = 3$

Step 3: Solve for $x$

Substitute $y = 3$ into equation (3): $x = 3 + 1$ $x = 4$

Final Solution

The solution to the system of equations is: $(x, y) = (4, 3)$

Would you like a deeper explanation or have any questions about this solution?

Related Questions:

1. Can the substitution method always solve systems of equations? Why or why not?
2. How does this method compare to elimination for solving the same system?
3. What happens if the equations are dependent (have infinite solutions)?
4. Can you graph these equations to verify the solution?
5. How do substitution and elimination methods handle systems with no solutions?

Tip:

When using substitution,