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### 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: 3x + 2y = 27 and x + y = 10, check the given equations inconsistent or consistentconsistentinconsistent Q 2: x + 2y = 10 and 3x + 4y = 22, check the given equations inconsistent or consistent.consistentinconsistent Q 3: 4x + 4y = 6 and 5x + 5y = 14, check the given equations inconsistent or consistent.consistentinconsistent Q 4: Solve the system graphically and choose the correct answer: 2y = 4x - 4 -8x + 4y = -8lines are parallellines coincidelines meet at one point Q 5: 2x + 2y = 4 and 3x + 3y = 3, check the given equations inconsistent or consistent.consistentinconsistent Q 6: Solve the system graphically and choose the correct answer: 3x + y = 5 x - y = 7inconsistentconsistent Q 7: Solve the system graphically and choose the correct answer: y - x = 3 y + 2x = -3lines coincidelines are parallellines meet at one point Q 8: 3x + 3y = 14 and 4x + 4y = 18, check the given equations inconsistent or consistent.consistentinconsistent Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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