Question

How do you solve the following system?: `x-7y=9 , 7y=3x+1`

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`x - 7y = 9`

`x - 7y + color(red)(7y) = 9 + color(red)(7y)`

`x - 0 = 9 + 7y`

`x = 9 + 7y`

Step 2) Substitute `9 + 7y` for `x` in the second equation and solve for `y`:

`7y = 3x + 1` becomes:

`7y = 3(9 + 7y) + 1`

`7y = (3 * 9) + (3 * 7y) + 1`

`7y = 27 + 21y + 1`

`7y = 28 + 21y`

`7y - color(red)(21y) = 28 + 21y - color(red)(21y)`

`(7 - color(red)(21))y = 28 + 0`

`-14y = 28`

`(-14y)/color(red)(-14) = 28/color(red)(-14)`

`(color(red)(cancel(color(black)(-14)))y)/cancel(color(red)(-14)) = -2`

`y = -2`

Step 3) Substitute `-2` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 9 + 7y` becomes:

`x = 9 + (7 * -2)`

`x = 9 + (-14)`

`x = 9 - 14`

`x = -5`

The solution is: `x = -5` and `y = -2` or `(-5, -2)`