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

Jun 18, 2015

$4 x + 14 y = - 10$ or $2 x + 7 y = - 5$

#### 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: $A x + B y = C$

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

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

$4 x + 14 y = - 10$

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 $\frac{1}{2}$, I get smaller numbers:

$\frac{1}{2} \left(4 x + 14 y\right) = \frac{1}{2} \left(- 10\right)$

$\frac{1}{2} \cdot 4 x + \frac{1}{2} \cdot 12 y = - 5$

$2 x + 7 y = - 5$