Name: ___________________

Date:___________________

kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

High School Mathematics
1.21 Linear Equations in Two Variables- Solving by the Method of Substitution

Method:
  1. Solve one of the equations for one variable in terms of the other.
  2. Substitute that expression found in step 1 into the other equation to obtain an equation in one variable.
  3. Solve the equation obtained in step 2
  4. Back substitute the solution in step 3 into the expression obtained in step 1 to find the value of the other variable
  5. Check that the solution satisfies each of the original equations
Example:
Solve the same system of equations by the method of substitution.
2x + y = 4 ----- Equation 1
x − y = −1 ------- Equation 2
Solution:
Take equation 1: 2x + y = 4 ----- Equation 1
2x + y = 4
y = 4 - 2x
Substituting y in equation 2
x − y = −1 ------- Equation 2
x − (4 − 2x) = −1
Solving for x
x − 4 + 2x = −1
3x = −1 + 4
3x = 3
x = 1
To find y, substitute x = 1 in equation 1 2x + y = 4 ----- Equation 1
2x + y = 4
2(1) + y = 4
2 + y = 4
y = 4 - 2
y = 2
x = 1 and y = 2
Answer: (1,2)
Directions: Solve the linear equations by the method of substitution. Also write at least 5 examples of your own.
Q 1: Solve the system by the method of substitution
7x + 2y = 16
21x 6y = 24
inconsistant
(3,-4)
(4,9)
(13,9)

Q 2: Solve the system by the method of substitution
x − y = 2
2x + y = 10
(4,2)
(2,3)
(2,4)
inconsistant

Q 3: Solve the system by the method of substitution
x - 3y = -2
5x + 3y = 17
(4/3,5/3)
(1/2.2/3)
(5/2,3/2)
inconsistant

Q 4: Solve the system by the method of substitution
2y + x = 3
4y 3x = 1
inconsistant
(1,1)
(0,2)
(1,7)

Q 5: Solve the system by the method of substitution
-x + 2y = 2
3x + y = 15
(2,4)
(4,3)
(3,5)
(1,2)

Q 6: Solve the system by the method of substitution
x + y = 4
x - y = 2
(1,4)
(2,1)
inconsistant
(3,1)

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


Subscription to kwizNET Learning System costs less than $1 per month & offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements


© 2003-2007 kwizNET Learning System LLC. All rights reserved. This material may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder. For permission, contact info@kwizNET.com
For unlimited printable worksheets & more, go to http://www.kwizNET.com.