Question

How do you solve using gaussian elimination or gauss-jordan elimination, `-2x -3y = -7`, `5x - 16 = -6y`?

Answer 1

So `x = 10/3` and `y = 1/9`

Explanation:

You have
`[(-2,-3,|-color(white)(0)7),(5,-6,|color(white)(-)16)]`

After a quick switch of the last equation to a `ax + by = c` format, now we want

`[(1,0,|h),(0,1,|q)]`

So we know `x = h` and `y = q` as solutions.

Adding `5/2L_1` to `L_2` we have

`[(-2,-3,|-color(white)(0)7color(white)(+5/2(-7))),(5+5/2(-2),-6+5/2(-3),|color(white)(-)16+5/2(-7))]`

`[(-2,-3,|-color(white)(0)7),(0,-27/2,|color(white)()-3/2)]`

Multiplying `L_2` by `2`

`[(-2,-3,|color(white)(0)-7),(0,-27,|color(white)(0)-3)]`

Add `-1/9L_2` to `L_1`

`[(-2-0,-3+3,|color(white)(0)-7+1/3),(0,-27,|color(white)(0)-3)]`

`[(-2,0,|color(white)(0)-20/3),(0,-27,|color(white)(0)-3)]`

Multiply `L_1` by `-1/2`

`[(1,0,|color(white)(0)10/3),(0,-27,|color(white)(0)-3)]`

Multiply `L_2` by `-1/27`

`[(1,0,|color(white)(0)10/3),(0,1,|color(white)(0)1/9)]`

So `x = 10/3` and `y = 1/9`