Question

How do you write `-7y - 10x + 11 = 0` in standard form?

Answer 1

See a solution process below:

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

First, subtract `color(red)(11)` from each side of the equation to isolate the `x` and `y` terms on the left side of the equation and the constant on the right side of the equation while keeping the equation balanced:

`-7y - 10x + 11 - color(red)(11) = 0 - color(red)(11)`

`-7y - 10x + 0 = -11`

`-7y - 10x = -11`

Next, rearrange the terms on the left side of the equation so the `x` term is first:

`-10x - 7y = -11`

Now, multiply each side of the equation by `color(red)(-1)` so the coefficient of the `x` term is non-negative while keeping the equation balanced:

`color(red)(-1)(-10x - 7y) = color(red)(-1) xx -11`

`(color(red)(-1) xx -10x) + (color(red)(-1) xx -7y) = 11`

`color(red)(10)x + color(blue)(7)y = color(green)(11)`