Alissa G.

asked • 10/22/16# solve question by elimination

a+b+c=-3

#### 3b-c=4

2a-b-2c=-5

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## 1 Expert Answer

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

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

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Ismael A.

You can quickly check with a calculator that the final solution is not correct. Considering just c in the final solution, the correct value is c=7/5

10/22/16