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January 3rd, 2016, 04:03 PM   #1
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Angry I have to solve 3 equations with 3 variables and I'm extremely confused

the three equations are:
4x + 3y -z = 4
2x - 9y - 7z = 8
(0x) + 2y + 6z = 0

I have gotten to the point of understanding that I need to combine two of the equations and to also eliminate one variable.

One of the biggest issues is I don't understand "(0x)," I've never seen that before. I feel like once I understand what that is I will be able to solve this problem.
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January 3rd, 2016, 04:18 PM   #2
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That means $x$ multiplied by 0. Essentially you can ignore it and leave the equation as $2y + 6z = 0$.
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January 3rd, 2016, 04:26 PM   #3
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From the first equation, 8x + 6y - 2z = 8.
Adding the second equation gives 10x - 3y - 9z = 16.
From the third equation, -3y - 9z = 0, so 10x = 16.
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January 3rd, 2016, 04:32 PM   #4
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what do you mean "from the first equation?" Aren't I supposed to add two equations together?
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January 3rd, 2016, 04:50 PM   #5
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so I tried adding the first two equations and got: 6x - 6y - 6z = 12
adding the last two I get: 2x - 7y - z = 8

when I try to combine the two I get: 8x + y - 5z = 20

I don't know what to do with that because I thought I was supposed to get rid of one of the variables...

(sorry I'm self-learning)
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January 3rd, 2016, 05:25 PM   #6
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I doubled the first equation, then added the second equation to the result.

That enabled me to use the third equation to eliminate the variables y and z together,
leaving 10x = 16, i.e., x = 1.6.

After you obtained 2x - 7y - z = 8, you could subtract the first equation to get -2x - 10y = 4,
which implies y = (-2x - 4)/10 = (-3.2 - 4)/10 = -0/72.

You made a slip when you added the first two equations.
You should have got 6x - 6y - 8z = 12.
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January 3rd, 2016, 05:25 PM   #7
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so whenever I do this I should always double the first equation that I try to combine?
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January 3rd, 2016, 05:27 PM   #8
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No, one normally eliminates one variable at a time, but I noticed a way to eliminate y and z together.
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January 3rd, 2016, 05:32 PM   #9
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(sorry if I'm being a pest)

How did you get the idea to subtract 2x - 7y - z = 8 from the first equation?
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January 3rd, 2016, 05:58 PM   #10
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I did that to eliminate z. There are other ways to eliminate z.

Many solvers would have solved by using the following method, which I give for comparison purposes.

From the third equation, y = -3z.

Substituting -3z for y in the first two equations gives 4x - 9z - z = 4 and 2x + 27z - 7z = 8,
so 4x - 10z = 4 and 2x + 20z = 8.

Doubling the first of those equations and then adding the second gives 10x = 16, as obtained before,
allowing one to say 4(1.6) - 10z = 4, so that z = (4(1.6) - 4)/10 = 0.24, and then y = -3z = -0.72.

Alternatively, doubling the second and then subtracting the first would give 50z = 12, so z = 0.24.
Again, y = -3z = -0.72, and x can be calculated as (4 + 10z)/4 = 6.4/4 = 1.6.
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