Question

How do solve the following linear system?: `-4x-14y=28 , x-2y=8`?

Answer 1

See the entire solution process below:

Explanation:

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

`x - 2y = 8`

`x - 2y + color(red)(2y) = 8 + color(red)(2y)`

`x - 0 = 8 + 2y`

`x = 8 + 2y`

Step 2) Substitute `8 + 2y` for `x` in the first equation and solve for `y`:

`-4x - 14y = 28` becomes:

`-4(8 + 2y) - 14y = 28`

`(-4 xx 8) + (-4 xx 2y) - 14y = 28`

`-32 - 8y - 14y = 28`

`-32 - 22y = 28`

`color(red)(32) - 32 - 22y = color(red)(32) + 28`

`0 - 22y = 60`

`-22y = 60`

`(-22y)/color(red)(-22) = 60/color(red)(-22)`

`(color(red)(cancel(color(black)(-22)))y)/cancel(color(red)(-22)) = (2 xx 30)/color(red)(2 xx -11)`

`y = (color(red)(cancel(color(black)(2))) xx 30)/color(red)(cancel(2) xx -11)`

`y = -30/11`

Step 3) Substitute `-30/11` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 8 + 2y` becomes:

`x = 8 + (2 xx -30/11)`

`x = (11/11 xx 8) - 60/11`

`x = 88/11 - 60/11`

`x = (88 - 60)/11`

`x = 28/11`

The solution is: `x = 28/11` and `y = -30/11` or `(28/11, -30/11)`