Question

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

Answer 1

`4x+14y=-10` or `2x+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=C`

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

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

`4x+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 `1/2`, I get smaller numbers:

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

`1/2 * 4x +1/2 *12y = -5`

`2x+7y=-5`