How do you put 7x+14y=3x-107x+14y=3x−10 into standard form?

1 Answer
Jim H
Jun 18, 2015

4x+14y=-104x+14y=−10 or 2x+7y=-52x+7y=−5

Explanation:

I was taught, and have taught out a quite a few textbooks that teach, that standard form for a linear equation in two variables is: Ax+By=CAx+By=C

Starting with 7x +14y = 3x-107x+14y=3x−10 we need to get all of the term involving the variables on the left. Subtract 3x3x from both sides to get:

7x-3x+14y = 3x-3x-107x−3x+14y=3x−3x−10 which simplifies to:

4x+14y = -104x+14y=−10

The weakness of standard from is that it is not unique. Every line has infinitely many standard from equations. If I multiply both sides of the equation above by 1/212, I get smaller numbers:

1/2(4x+14y) = 1/2(-10)12(4x+14y)=12(−10)

1/2 * 4x +1/2 *12y = -512⋅4x+12⋅12y=−5

2x+7y=-52x+7y=−5

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