Choose the best description of the system.

label Algebra
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{5x-3y=6

{-20x+12y=-21

Select all that apply. (a) consistent  (b) inconsistent  (c) independent  (d) dependent

Jul 29th, 2014

For reference: Inconsistent is when no intersection no solution occurs, Consistent is when we have a solution, independent is when there is one solution, dependent is when we have infinite solutions and the two equations are the same line. 

First add 4 times the first eqn to the 2nd. We obtain: 0x+0y=3

Since 0 cannot equal 3. It is likely the equations are parallel. Ignore the constants on the right. We see that Eqn2=4Eqn1 (ignoring the constants)...this means the lines have the same slope. The constants on the right are different so this means that the lines are NOT the same line. 

Lines that are parallel and not the same line will not intersect and have 0 solutions. Therefore the system is inconsistent (A).

When we graph them we see that they are indeed parallel. Graph 2.PNG

Jul 29th, 2014

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