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Middle/High School Algebra, Geometry, and Statistics (AGS)
1.21 Solving Equations - Substitution Method I

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 = 12-3y
x = (12-3y)/2 -------(3)
Substitute the value of x in equation (1)
3[(12-3y)/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 = (12-6) / 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.

Name: ___________________

Date:___________________

Middle/High School Algebra, Geometry, and Statistics (AGS)
1.21 Solving Equations - Substitution Method I

Q 1: Solve 2x + 4y = 10 and 3x + 2y = 7.
x = 1 and y = 2
x = 4 and y = 3
x = 3 and y = 4
x = 2 and y = 1

Q 2: Solve 2x + 5y = 26 and 3x + 7y = 37.
x = 5 and y = 2
x = 2 and y = 5
x = 3 and y = 4
x = 4 and y = 3

Q 3: Solve 3x + 2y = 11 and 2x + 6y = 12.
x = 2 and y = 4
x = 3 and y = 1
x = 1 and y = 3
x = 4 and y = 2

Q 4: Solve 4x + 5y = 50 and 3x + 2y = 27.
x = 5 and y = 6
x = 7 and y = 5
x = 6 and y = 5
x = 5 and y = 7

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Question 6: This question is available to subscribers only!


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