Method of Substitution
In this method we express one variable in terms of the other variable in one
of the equations and solve the resulting equation for another value.
Example:
Solve 3x + 2y = 13 and 2x + 3y = 12.
Solution:
Given that 3x + 2y = 13 (1)
2x + 3y = 12(2)
Find the value of x in terms of y.
2x + 3y = 12
2x = 123y
x = (123y)/2 (3)
Substitute the value of x in equation (1)
3[(123y)/2] + 2y = 13
Multiplying on both sides by 2, we get
3(12  3y) + 2 * 2y = 2 * 13
36  6y +4y = 26
36  5y = 26
5y = 26  36
5y = 10
y = 10 / 5
y = 2
Substitute the value of y in equation (3), we get the value of x.
x = (12  3 * 2) / 2
x = (126) / 2
x = 6/2
x = 3
Therefore, Solution set = {(3,2)}
Verification:
We have to verify the solution (3,2) satisfies both equations or not.
3x + 2y = 13 and 2x + 3y = 12
3 * 3 + 2 * 2 = 13 and 2 * 3 + 3 * 2 = 12
9 + 4 = 13 and 6 + 6 = 12
13 = 13 and 12 = 12
Therefore, The solution (3,2) is correct.
Directions: Choose the correct answer. Also write at least ten examples of your own.
