solve question by elimination

Question

a+b+c=-3

3b-c=4

2a-b-2c=-5

Answer 1

Hi Alissa,

 

I'm going to number the equations as I go.

 

1)    a+b+c=-3

2)       3b-c= 4

3)    2a-b-2c=-5

 

Since equation 2) does not have an "a" term.  Let's bring equations 1) and 3) together and see if we can eliminate the "a" term.

 

1) a+b+c=-3
3) 2a-b-2c=-5

 

To do this, multiply equation 1) by -2.  We'll call this equation 4).

 

4) -2a-2b-2c=6

3) 2a-b-2c=-5

 

Add together equations 4) and 3), term by term.  We'll call this equation 5).

 

5) -3b-4c = 1

 

Now let's look at equation 5) and equation 2)

 

2)   3b-c =  4

5) -3b-4c = 1

 

Since equation 2) has a coefficient of 3 for the "b" term and equation 5) has a coefficient of -3 for the "b" term, we can add these two equations together term by term.  We'll call this equation 6).

 

6) -5c = 5

Now we can solve for "c" by dividing both sides by -5.

We have c = -1

 

With c=-1, go back to equation 2) using and solve for "b".

2) 3b-c = 4

    3b-(-1) = 4

    3b = 3

    b = 1

 

So we have b=1 and c=-1

 

Finally, using equation 1) we can solve for "a" using the values we have for "b" and "c".

 

1)    a+b+c=-3

       a+1+(-1) = -3

       a+0=-3

       a=-3

 

The final solution is

a= -3

b= 1

c= -1