Question

How do you write `-3x+y=6` in standard form?

Answer 1

`color(red)(3)x - color(blue)(1)y = color(green)(-6)`

Explanation:

The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform this to standard form we need to multiply both sides of the equation by `color(purple)(-1)`

`color(purple)(-1)(-3x + y) = color(purple)(-1) xx 6`

`(color(purple)(-1) xx -3x) + (color(purple)(-1) xx y) = -6`

`color(red)(3)x - color(blue)(1)y = color(green)(-6)`