How do you solve the following system?: #8x +6y =9 , - 5x -7y = -2#

2 Answers
May 3, 2017

Answer:

With some arrangement. #x=51/26# and #y=-29/26#

Explanation:

Expand the first equation with term 5
Expand the second equation with 8.

Now you have:

#40x+30y=45#
#-40x-56y=-16#
Now sum these up:
#-26y=29#

or #y=-29/26#

Now you can find x using the first or second equation:

#8x-(6*29)/26=9#

#8x=9+(6*29)/26#

#8x=(117/13) + ((3*29)/13)#

#8x=204/13#

#x=204/104#

or

#x=51/26#

Answer:

#x = 1 25/26#, #y = -1 21/182#

Explanation:

#8x + 6y = 9# ....................(i)
#-5x - 7y = -2# ....................(ii)

You can solve this system by using Elimination method.

You can eliminate either #x# or #y# here.
I will eliminate #x#.

So multiplying eq.(i) by #+5# and eq(ii) by #+8#, you will get

#40x + 30y = 45# ......................(iii) &
#-40x - 56y = -16# ........................(iv)

Adding eq (iii) and (iv), you will get

#-26y = 29#

#rArr# #y = -29/26#

Substituting #y = -29/26# in eq(i), you will get

#8x + (-29/26)*6 = 9#

#rArr# #8x = 9 + 87/13#

#rArr# #8x = (117 + 87)/13 #

#rArr# #8x = 204/13#

#rArr# #x = 204/104 = 51/26#