How do you solve the following system?: # -2x +5y =-6 , 3x +2y = -1#

1 Answer
Aug 15, 2016

Answer:

#x = 7/19 and y = -20/19#

Explanation:

As the x-terms have different signs, we will eliminate them by using an LCM of 6 and adding.

# -2x +5y =-6#.............................................. A

# 3x +2y = -1#....................................................B

Ax3: #-6x+15y = -18#.......... ......................................C

Bx2: #" "6x+4y=-2#........................................................D

C+D:#" " 19y= -20#

#y = (-20)/19#

Substitute #(-20)/19# for y in B

#3x + 2((-20)/19) = -1 " "xx19#

#19xx3x + (-40)/19xx19 = -1xx19#

#57x-40 = -19#

#57x = 21#

#x = 21/57 = 7/19#

Check in A

# (-2xx7)/19 +(5xx(-20))/19#

#(-14-100)/19#

#-114/19#

=#-6#