Question

How do solve the following linear system?: `x+2y =2 , x - 3y = -6`?

Answer 1

Using substitution I have found the answer below.

Explanation:

x + 2y = 2
x = 2 - 2y
2 - 2y - 3y = -6
2 - 5y = -6
-5y = -8
y = `8/5`

x + 2(`8/5`) = 2
x + `16/5` = 2
x = `-6/5`

The solution set is (`-6/5`, `8/5`)

Answer 2

`x = -1.2 " and " y = 1.6`

Explanation:

First, we need to isolate one variable - `x` in this case:
`x +2y = 2` becomes `x = 2 - 2y`.
Then, we take this "new value" of x and put in the second equation:
`(2 - 2y) -3y = -6` which becomes `y = 8/5 " or " 1.6` when solved.
Having this new value of `y`, we go back to the first equation and solve it, finding `x` :
`x = 2 - 16/5 = 10/5 - 16/5 = -6/5 " or" - 1.2`