Sure! The substitution method is a technique for solving systems of linear equations. Here's a step-by-step explanation using the problem we just solved as an example.

Substitution Method Steps

1. Identify the system of equations: We start with two equations involving two variables. In our case, the system is: $A + B = 26$ $A = B + 8$

2. Solve one equation for one variable: Choose one of the equations and solve it for one of the variables. We already have the second equation solved for $A$: $A = B + 8$

3. Substitute the expression into the other equation: Substitute the expression obtained in step 2 into the other equation. This eliminates one variable, allowing you to solve for the remaining variable. Substitute $A$ in the first equation: $(B + 8) + B = 26$

4. Simplify and solve the resulting equation: Simplify the equation and solve for the variable: $B + 8 + B = 26$ $2B + 8 = 26$ $2B = 18$ $B = 9$

5. Substitute back to find the other variable: Use the value of the variable obtained in step 4 and substitute it back into one of the original equations to find the value of the other variable. Substitute $B = 9$ into $A = B + 8$: $A = 9 + 8$ $A = 17$

6. Check the solution: Verify the solution by substituting both values back into the original equations to ensure they are satisfied: $A + B = 26 \implies 17 + 9 = 26$ $A = B + 8 \implies 17 = 9 + 8$ Both equations are true, so the solution is correct.

Summary

• Step 1: Write down the system of equations.
• Step 2: Solve one equation for one variable.
• Step 3: Substitute that expression into the other equation.
• Step 4: Solve for the remaining variable.
• Step 5: Substitute back to find the other variable.
• Step 6: Check your solution.

Would you like any more details or have another question?

Here are 5 questions you can ask:

1. How do you solve systems of equations using the elimination method?
2. What are some real-life applications of solving systems of equations?
3. Can you explain the graphing method for solving systems of equations?
4. What are some common mistakes to avoid when solving systems of equations?
5. How can you solve systems of equations with more than two variables?

Tip: When using the substitution method, always double-check your work by substituting the solution back into the original equations to verify its correctness.