How do solve the following linear system?: # 7x-2y=8 , 3x – 4y = 7 #?

1 Answer
Dec 24, 2015

Answer:

By substitution or by elimination

Explanation:

you are given a 2 equation and you need to find both x and y

#{(7x-2y=8), (3x-4y=7) :}#

there are two solutions and they have both the same answer. you will just choose what is easier.

By substitution
first let's find the value of x in first equation

#7x-2y=8#

#7x=8+2y -># transpose #2y# to other side of equation to leave #7x#

#x= (8+2y)/7 -># divide both side by #7#

then we have the x value

substitute your answer (the value of #x#) to next equation

#3 * ((8+2y)/7) - 4y = 7#

#(24+6y)/7 - 4y = 7#

#(24+6y)/7 - 4y = 7 | * (7)#

#24+6y-28y=49#

#-22y=49-24#

#-22y=25#

#y=-25/22#

To find the value of #x# just substitute the first equation by the value of #y#.

BY ELIMINATION

#{(7x-2y=8), (3x-4y=7) :}#

Think of how to eliminate any one of the variables.

i think that if we multiply the first equation by #-2#, #y# will be cancelled.

#{((7x-2y=8) | * (-2)), (3x-4y=7):}#

#-14x + 4y = -16#
#" "3x - 4y =7#

Add the two equations to get

#-14x + cancel(4y) + 3x - cancel(4y) = -16 + 7#

#-11x=-9 -># divide both sides by #-11#

#x=9/11#

To know the value of #y#, substitute the value of #x# in one of the equation.

#3x-4y=7#

#3 * (9/11) - 4y=7#

#27/11 - 4y = 7#

#-4y=7 - 27/11#

#-4y=50/11 -># divide both sides by #-4#

#y=-25/22#