How do you solve the system of equations #8x + 4y = 84# and #9x - 9y = 54#?

3 Answers

Answer:

#x=9, \ \ y=3#

Explanation:

Given equations

#8x+4y=84#

#2x+y=21\ ..........(1)# &

#9x-9y=54#

#x-y=6\ ..........(2)#

Adding (1) & (2), we get

#2x+y+x-y=21+6#

#3x=27#

#x=27/3#

#x=9#

setting #x=9# in (1), we get

#2(9)+y=21#

#y=21-18#

#y=3#

hence the solution of given equations is

#x=9, \ \ y=3#

Jul 24, 2018

Let's solve the first equation first

#8x+4y=84#

All you have to do is take out the value of a variable

Let's take out the value of #y# both #x# and #y# will be irritating in the next equation but #y# will be less irritating (maybe)

Factorize out 4 and divide

#4(2x+y)=84#

#2x+y=21#

#color(red)(y=21-2x#

Now to the second equation

#9x-9y=54#

Factorize out #9#

#9(x-y)=54#

#x-y=6#

Put value of #y#

#x-(21-2x)=6#

Notice that after opening the brackets the values will go from plus to minus and from minus to plus

#x-21+2x=6#

#3x-21=6#

#3x=6+21#

#3x= 27#

#x=27/3#

#color(darkorange)(x=9#

#y=21-2x#

#y=21-2xx9#

#y=21-18#

#color(darkorange)(y=3#

Jul 24, 2018

Answer:

#x=9# and #y=3#

Explanation:

#9*(8x+4y)+4*(9x-9y)=9*84+4*54#

#72x+36y+36x-36y=756+216#

#108x=972#, so #x=972/108=9#

Thus,

#9*9-9y=54#

#81-9y=54#

#-9y=-27#

#y=(-27)/(-9)=3#