How to solve these equations by using elimination method to find the x value and y value: 3x-y= -6 and 2x-y=0   x-3y=27 and 2x-y=9

Expert Answers
hala718 eNotes educator| Certified Educator

3x-y=-6...(1)

2x-y =0....(2)

To solve using the elimination method, we need to eliminate one of the variables by adding of subtracting equations

By subtracting (2) from (1) we get:

3x-y -2x-(-y) = -6-0

x = -6

==> by substituting x in either equations:

2x-y=0

2(-6)-y=0

-12 -y=0

y=-12

 

Now for x-3y=27....(1)

and       2x-y=9......(1)

Let us multiply (1) with -2 and add to (1)

==> -2x+6y= -54

==> 2x -y =9

==> 5y = -45

==> y= -9

Now x-3y=27   substitute with x=-9

==> -9 -3y= 27

==> -3y= 36

==> y = -12

 

 

rnk | Student

(1)

3x - y = -6

2x - y = 0

(-) (+) 

===========

x =   -6

2x-y=0

=>y=2x = 2(-12) = -24

(2)

x - 3y = 27

Multiplying with 2 we get,

2x - 6y = 54

2x - y =   9

(-) (+)    (-)

=============

-5y = 45

therefore y = 45/(-5) = -9

x - 3y = 27

x - 3(-9)= 27 

x + 27 = 27

therefore x = 27 - 27 = 0