Question

How do solve the following linear system?: `x+2y=1 , 6 x+3y=11`?

Answer 1

See a 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) Substitute `(1 - 2y)` for `x` in the second equation and solve for `y`:

`6x + 3y = 11` becomes:

`6(1 - 2y) + 3y = 11`

`(6 * 1) - (6 * 2y) + 3y = 11`

`6 - 12y + 3y = 11`

`6 + (-12 + 3)y = 11`

`6 + (-9)y = 11`

`6 - 9y = 11`

`6 - color(red)(6) - 9y = 11 - color(red)(6)`

`0 - 9y = 5`

`-9y = 5`

`(-9y)/color(red)(-9) = 5/color(red)(-9)`

`(color(red)(cancel(color(black)(-9)))y)/cancel(color(red)(-9)) = -5/9`

`y = -5/9`

Step 3) Substitute `-5/9` 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 * -5/9)`

`x = 1 - (-10/9)`

`x = 1 + 10/9`

`x = 9/9 + 10/9`

`x = 19/9`

The Solution Is:

`x = 19/9` and `y = -5/9`

Or

`(19/9, -5/9)`