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How do you set up and solve the following system using augmented matrices #3x-2y=8, 6x-4y=1#?

Answer 1

Liam Brennan

No solution

The typesetting here does not support row augmented matrices.

But, if we are going with: #3x-2y=8, 6x-4y=1# ...then we start with:

#((3, -2),(6, -4))((8),(1))#

However, there is an immediate problem, we have linearly dependent rows, this is a singular matrix :(

#((3, -2),(6, -4)) = ((1/2(6), 1/2(-4)),(6, -4))#

So this either has no solutions or infinitely many:

#((3, -2),(6, -4)) ((x),(y)) = ((8),(1))#

Then go back and look at the equations and you will see that they represent parallel lines:

#3x-2y=color(red)(8)#

# 2(3x)-2(2y)=color(blue)(2(1/2))#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.