How do you solve the following system?: #-3x -2y =13, 7x -7y = -3#

1 Answer
Sep 23, 2017

Answer:

#x = - ( 97)/ (35)# and # y = - 82 / 35#

Explanation:

The given set of equation is

#-3x -2y =13 # --------------(1)

and

# 7x -7y = -3# --------------(2)

Make the coefficient of any one variable same in both equations.
So we will multiply equation(1) by 7 and equation (2) by 3

(1) x 7 gives :

# - 21x -14y = 91#

(2) x 3 gives:

# 21x - 21y = -9#

Now, as the coefficients of # x # in both the new equations are same but opposite in sign, we will add the two equations so that #x # gets eliminated and we can find value of y

# (- 21x -14y = 91 ) #
+ # (21x - 21y = -9)#

That gives :
# -35 y = 82#
# y = - 82 / 35#

Substituting this value of #y# in any one equation , we can find value of #x#

#-3x -2y =13 # --------------(1)

#-3x -2(-82/ 35) =13 #

#-3x + (164/35) =13 #

#-3x = 13 - (164/35)#

#-3x =( (13)*(35) - (164))/ 35#

#-3x =( 455 - 164)/ 35#

#-3x =( 291)/ 35#

#x =( 291)/ (35 * (-3))#

#x = - ( 97)/ (35)#

Therefore #x = - ( 97)/ (35)# and # y = - 82 / 35#