Question

How do you find the x and y intercept of `7x + 3y = –21`?

Answer 1

See the entire solution process below:

Explanation:

To find the `x` intercept by substitution you substitute `0` for `y` and solve for `x`:

`7x + 3y = -21` becomes:

`7x + (3 xx 0) = -21`

`7x + 0 = -21`

`7x = -21`

`(7x)/color(red)(7) = -21/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = -3`

`x = -3` so the x-intercept is `-3` or `(-3, 0)`

To find the `y` intercept by substitution you substitute `0` for `x` and solve for `y`:

`7x + 3y = -21` becomes:

`(7 xx 0) + 3y = -21`

`0 + 3y = -21`

`3y = -21`

`(3y)/color(red)(3) = -21/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -7`

`y = -7` so the y-intercept is `-7` or `(0, -7)`