How do you solve #5x + 4y = 6# and #-2x - 3y = -1#?

1 Answer
Aug 10, 2015

Answer:

#(x,y) = (2,-1)#

Explanation:

[1]#color(white)("XXXX")##5x+4y=6#
[2]#color(white)("XXXX")##-2x-3y=-1#

Multiply [1] by 2 and [2] by #(-5)# to get 2 equations with identical coefficients for #x#
[3]#color(white)("XXXX")##10x+8y = 12#
[4]#color(white)("XXXX")##10x+15y=5#

Subtract [4] from [3]
[5]#color(white)("XXXX")##-7y = 7#

Divide both sides by #(-7)#
[6]#color(white)("XXXX")##y = -1#

Substitute #(-1)# for #y# in [1]
[7]#color(white)("XXXX")##5x+4(-1) = 6#

Simplify
[8]#color(white)("XXXX")##x = 2#