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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

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 intersectionInfinitely many points No point of intersection
One solutionMany 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 = 8 and 2x + 3y = 13, check the given equations inconsistent or consistent.
consistent
inconsistent

 Q 2: Solve the system graphically and choose the correct answer:
y - x = 3
y + 2x = -3
lines coincide
lines meet at one point
lines are parallel

Q 3: 3x + 3y = 14 and 4x + 4y = 18, check the given equations inconsistent or consistent.
consistent
inconsistent

 Q 4: Solve the system graphically and choose the correct answer:
3x + y = 5
x - y = 7
consistent
inconsistent

Q 5: Solve the system graphically and choose the correct answer:
2y - x = 4
4y = 2x + 12
lines meet at one point
lines coincide
lines are parallel

 Q 6: Solve the system graphically and choose the correct answer:
3x - 4y = 13
2x + y = 5
consistent
inconsistent

Q 7: 4x + 4y = 6 and 5x + 5y = 14, check the given equations inconsistent or consistent.
consistent
inconsistent

 Q 8: x + 2y = 10 and 3x + 4y = 22, check the given equations inconsistent or consistent.
consistent
inconsistent

Question 9: This question is available to subscribers only!

 Question 10: This question is available to subscribers only!


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