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

1 Answer
Jan 14, 2016

Answer:

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#