Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x - 3y = 5`, `3x + 4y = -1`?

Answer 1

`x=1, y=-1`

Explanation:

We can write the system of linear equation in matrix vector form

`A ulx = ulb`

`( (2,-3), (3,4) ) ( (x), (y) ) = ( (5), (-1) )`

So the Augmented Matrix is:

`( (2,-3,|,5), (3,4,|,-1) )`

We can now perform elementary row operations:

`( (2,-3,|,5), (3,4,|,-1) ) stackrel(1/2R_1 rarr R_1)(rarr) ( (1,-3/2,|,5/2), (3,4,|,-1) )`

`( (1,-3/2,|,5/2), (3,4,|,-1) ) stackrel(R_2-3R_1 rarr R_2)(rarr) ( (1,-3/2,|,5/2), (0,17/2,|,-17/2) )`

And so:
`17/2y=-17/2 => y=-1`

Back substituting into R1:
`x - 3y/2 = 5/2 => x+3/2=5/2 => x=1`