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

1 Answer
Nov 27, 2016

Answer:

# 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 #