Is 3x plus 2y equals 15 and 6x plus 4y equals 30 Consistent or inconsistent?

Answer 1

We will see.

3X + 2Y = 15

6X + 4Y = 30

I do not like the look of elimination, so substitution

3X + 2Y = 15

3X = 15 - 2Y

X = 5 - 2/3Y

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6(5 - 2/3Y) + 4Y = 30

30 - 12/3Y = 30

30 - 4Y = 30

this is inconsistent in approach

3(5 - 2/3Y) + 2Y = 15

15 - 15/3Y = 15

another bad approach, try elimination to show inconsistency

- 2(3X + 2Y = 15)

6X + 4Y + 30

-6X - 4Y = - 30

6X + 4Y = 30

I think it is safe to say these systems of equations are

inconsistent

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