2 x 2 system or linear equations that is inconsistent or consistent dependent

Algebra
Tutor: None Selected Time limit: 1 Day

Nov 21st, 2015

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-4x + y = -4 ---(1)

-4x - y = -4 ---(2)


Add equations (1) and (2)

-8x = -8

x = (-8)/(-8)

x = 1


Substitute value of x in equation (1)

-4*1 + y = -4

-4 + y = -4

y = -4 + 4

y = 0


So the system of equations has a unique solution 

and the solution is (1, 0).

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-2x + y = -8 ---(1)

2x = 8 + y ---(2)


From equation (2)

2x - y = 8

Multiply both sides by -1

-2x + y = -8


So both equations represent the same line and all the points on the line is a solution.

Hence the system of equations has infinitely many solutions.

They must satisfy y = 2x - 8

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Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 21st, 2015

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