SUBSTITUTION METHOD
Definition Of Substitution Method
Substitution method is a method of solving a system of equations wherein one of the equations is solved for one variable in terms of the other variables.
Video Examples: Solving Linear Systems Substitution Method
Solved Example on Substitution Method
Ques: Use the substitution method to solve the linear system.
Use the substitution method to solve the linear system.
5x + 3y = 26
x - 3y = 4
Choices:
Correct Answer: A
Solution:
Step 1: 5x + 3y = 26 [Equation 1.]
Step 2: x - 3y = 4 [Equation 2.]
Step 3: x = 3y + 4 [Rearrange equation 2.]
Step 4: 5(3y + 4) + 3y = 26 [Substitute the values.]
Step 5: 18y + 20 = 26 [Group the like terms.]
Step 6: 18y = 6 [Subtracting 20 from the two sides of the equation.]
Step 7: 
[Divide throughout by 18.]
Step 8: 
[Substitute the values.]
Step 9: x = 5 [Simplify.]
Step 10: The solution for the linear system is 
.
Quick Summary
- Solve one equation for one variable.
- Substitute the expression into the other equation.
- Solve for the remaining variable.
- Substitute back to find the value of the first variable.
🍎 Teacher Insights
Emphasize the importance of checking the solution by substituting the values back into both original equations. Encourage students to choose the easiest equation to solve for a variable to minimize errors.🎓 Prerequisites
- Solving linear equations
- Basic algebraic manipulation
- Understanding of variables
Check Your Knowledge
Q1: Solve the system: x + y = 5, x = 2y - 1
Q2: Solve the system: 2x - y = 3, x = y + 1
Frequently Asked Questions
Q: When is the substitution method most useful?
A: The substitution method is most useful when one of the equations is already solved for one variable or can be easily solved for one variable.
Q: Can the substitution method be used for non-linear systems of equations?
A: Yes, the substitution method can be used for non-linear systems of equations, but it may be more complex.