How do you solve the following system: #2x+7y=1, 6x + 7y = -9 #?

2 Answers
Jul 31, 2017

Answer:

By arranging it, it can be calculated that #x=-5/2# and #y=6/7#

Explanation:

The first equation can be rewritten
#-6x - 21y = -3# (after multiplication by -3)
#6x + 7y = -9# (the second original equation)

Combine these two equations:
#-14y = -12#

#y=12/14#
or
#y=6/7#

Now put value in the first original equation:

#2x = 1 - (7times(6/7))#

#2x = 1-6#

#x=-5/2#

The answer is #x=-5/2# and #y=6/7#

Jul 31, 2017

Answer:

#x= -2.5 and y= 6/7#

Explanation:

Note that the number of #y#s in both equations stays the same.
The difference in the the totals therefore represents the difference in the number of #x#s. Subtract the two equations:

#" "6xcolor(blue)(+7y) =-9" ".........A#
#" "ul(2xcolor(blue)(+7y) =+1)" ".........B#

#A-B" "4x = -10" "#solve for #x#

#" "x = -2.5#

Substitute #-2.5# for #x# to find #y# in B

#2(-2.5) +7y =1#

#" "-5 +7y = 1#
#" "7y =1+5#
#" "7y =6#
#" "y = 6/7#

Check in A:
#6xx(-2.5)+7(6/7)#

#=-15+6 =-9#
This is correct.