What are x and y if #7x+5y=18# and #-7x-9y=4#?

2 Answers
Alan P.
Oct 29, 2015

#(x,y) = (6 13/14, -5 1/2)#
#color(white)("XXX")#This may be wrong if I changed the first expression into the wrong equation, but it was meaningless as written

Explanation:

[1]#color(white)("XXX")7x+5y=18color(white)("XXXXXX")#note: I changed this from original version #7x+5y+18#
[2]#color(white)("XXX")-7x-9y=4#

Adding [1] and [2]
[3]#color(white)("XXX")-4y = 22#

Dividing both sides by #(-4)#
[4]#color(white)("XXX")y = -5 1/2#

Substituting #(-5 1/2)# for #y# in [1]
[5]#color(white)("XXX")7x+5(-5 1/2) =18#

Simplifying
[6]#color(white)("XXX")7x-27 1/2 = 18#

[7]#color(white)("XXX")7x = 45 1/2#

[8]#color(white)("XXX")x= 6 13/14#

Nallasivam V
Oct 29, 2015

#x=13/2#
#y =(-11)/2#

Explanation:

#7x+5y=18#----------------(1)
#-7x-9y=4#-----------------(2)

Since the co-efficients of #x# is # 7# and #-7#, we can eliminate #x# by adding the two equations.

#7x+5y=18#----------------(1) ADD with (2)
#-7x-9y=4#-----------------(2)

#-4y=22#
#y =22/(-4)=(-22)/4=(-11)/2#
#y =(-11)/2#

Substitute #y =(-11)/2# in equation (1)

#7x +5((-11)/2)=18#
#7x -55/2=18# Multiply both sides by 2
#14x-55=36#
#14x=36+55#
#14x=91#
#x=91/14=13/2#
#x=13/2#

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