Inequality classifications
x + 5y = −2 and x + 5y = 4 Inconsistent
y = 3x + 4 and −2x + y = 4 consistent and independent
3x + y = 4 and −6x − 2y = −8 consistent and dependent
What are inconsistent equations?
A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
x + 5y = −2
x + 5y = 4
subtracting gives
0 = -6 no solution
What are consistent and independent equations?
A system is deemed consistent if it has at least one solution.
A consistent system is independent if it only has one solution.
-3x + y = 4
−2x + y = 4
subtracting gives
-x = 0
x = 0
substituting x to get y
-3 * 0 + y = 4
y = 4
What are consistent and dependent equations?
A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.
3x + y = 4
−6x − 2y = −8
subtracting gives
9x + 3y = 12 - none cancels out meaning infinite number of possible solutions
Learn more on simultaneous equation here:
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