Name: ___________________Date:___________________

 Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

### Middle/High School Algebra, Geometry, and Statistics (AGS)1.24 Inconsistent Equations

A system of linear equations is called consistent if it has at least one solution, and it is called inconsistent if it has no solution.

 Consistent Consistent Inconsistent Two lines that intersect Two lines that coincide Two parallel lines One point of intersection Infinitely many points No point of intersection One solution Many solutions No solution Example: x + y = 7 x - y = 5 Example: x + y = 8 3x + 3y = 24 Example: x + y = 8 3x + 3y = 14

Let a1x + b1y + c1 = 0 and a2x+b2y+c2 = 0 are any two equations. a1 and a2 are the coefficients of x and b1 and b2 are the coefficients of y and c1 and c2 are the constants.
If a1b2 = a2b1, then the equations a1x + b1y + c1 = 0 and a2x+b2y+c2 = 0 are inconsistent equations.

Example:
x + y = 8 and 3x + 3y = 14, check the given equations inconsistent or not.
Solution:
Given that x + y = 8 and 3x + 3y = 14
Here a1 = 1 and a2 = 3
b1 = 1 and b2 = 3
a1b2 = a2b1
1 * 3 = 3 * 1
3 = 3
Therefore the given equations are inconsistent.

Directions: Solve the linear system graphically and determine whether the system is consistent and independent, inconsistent, consistent and dependent. Also write at least 10 examples of your own.
 Q 1: x + 2y = 10 and 3x + 4y = 22, check the given equations inconsistent or consistent.consistentinconsistent Q 2: 3x + 2y = 27 and x + y = 10, check the given equations inconsistent or consistentinconsistentconsistent Q 3: Solve the system graphically and choose the correct answer: 2y = 4x - 4 -8x + 4y = -8lines meet at one pointlines coincidelines are parallel Q 4: Solve the system graphically and choose the correct answer: 3x - 4y = 13 2x + y = 5inconsistentconsistent Q 5: Solve the system graphically and choose the correct answer: 3x + y = 5 x - y = 7consistentinconsistent Q 6: 2x + 2y = 4 and 3x + 3y = 3, check the given equations inconsistent or consistent.consistentinconsistent Q 7: 4x + 4y = 6 and 5x + 5y = 14, check the given equations inconsistent or consistent.consistentinconsistent Q 8: Solve the system graphically and choose the correct answer: y - x = 3 y + 2x = -3lines coincidelines are parallellines meet at one point Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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

• Instant scoring of online quizzes
• Progress tracking and award certificates to keep your student motivated
• Unlimited practice with auto-generated 'WIZ MATH' quizzes

© 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.