Question

How do solve the following linear system?: `x+2y=1 , -3x -8y = -9`?

Answer 1

x=-5 and y=3

Explanation:

`x+2y=1`
`x=1-2y` -----(1)

`-3x-8y =-9`
`3x + 8y = 9` -----(2)

Substituting (1) into (2):

`3(1-2y) + 8y = 9`
`2y +3 = 9`
`y = 3`

Substituting y=3 into (1):

`x= 1-2(3)= -5`

Answer 2

See the entire solution process below:

Explanation:

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

`x + 2y = 1`

`x + 2y - color(red)(2y) = 1 - color(red)(2y)`

`x + 0 = 1 - 2y`

`x = 1 - 2y`

Step 2) Subsitute `1 - 2y` for `x` in the second equation and solve for `y`:

`-3x - 8y = -9` becomes:

`-3(1 - 2y) - 8y = -9`

`(-3 * 1) - (-3 * 2y) - 8y = -9`

`-3 - (-6y) - 8y = -9`

`-3 + 6y - 8y = -9`

`-3 + (6 - 8)y = -9`

`-3 - 2y = -9`

`color(red)(3) - 3 - 2y = color(red)(3) - 9`

`0 - 2y = -6`

`-2y = -6`

`(-2y)/color(red)(-2) = -6/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 3`

`y = 3`

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

`x = 1 - 2y` becomes:

`x = 1 - (2 * 3)`

`x = 1 - 6`

`x = -5`

The solution is: `x = -5` and `y = 3` or `(-5, 3)`