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Algebra/3 variables

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Expert: Michael Tadesse - 9/17/2009


Question
QUESTION: Hi Michael,

trying to solve a triple equation with 3 variables;
3i+2j=9
j-4k=8
5i+3k=9

not sure whether to add first equation to each of the others?? which is the best method to eliminate the variables?

Kind regards,
Ria

ANSWER:  Hello Ria

First add the first and the third equations, because ‘i’ is common.
3i + 2j = 9
5i + 3k = 9

This means 3i + 2j and 5i + 3k are equal.
3i + 2j = 5i + 3k
2j – 3k = 5i – 3i
2j – 3k = 2i
(2j – 3k)/ 2 = i

Now substitute it in the third equation

5/2(2j – 3k) + 3k = 9
5j – 15/2k + 3k = 9
5j – 9/2k = 9 (multiply both sides by 2)
10j – 9k = 18

Then, solve it with the second equation

j- 4k=8
10j – 9k = 18

To cancel out j multiply the first equation by -10

-10j + 40k = -80
10j – 9k = 18

Now add them

0 +31k = -62
K = -2

It is a matter of substituting now.

Insert k in of the above equations and find j

10j – 9*-2 = 18
10j + 18 = 18
J = 0

Now substitute j in the first (very first) equation and find i
3i + 2j = 9
3i = 0 = 9
I = 3 so the solution is {i, j, k} = {3, 0, -2}


---------- FOLLOW-UP ----------

QUESTION: Hi Michael,

This is very well explained, I understand all the steps apart from the working out of one ie.
Now substitute (i)  in the third equation, I make it

5 x (2j-3k)/2   + 3k   = 9
10j - 15k/10    + 3k   = 9
2j  - 3k/2      + 3k   = 9
j   - 1.5k      + 3k   = 9
j   + 1.5k      + 3k   = 9
j   + 4.5k  = 9
multiply both sides by 2
2j  + 9k   =  18

Any idea where I've gone hopelessly wrong?

Thank you once again


Answer
Hello Ria,
Good to hear from you again. I see that you’re working well.

What I meant was

(5/2)*(2j-3k) + 3k = 9 ----------- you have to distribute and multiply everything in the bracket by 2.5 or 5/2) but you forgot to divide 10 by 2, you just put 10. I should be 5. and the second on should be
-15/2 or -7.5, but you wrote -15/10 or -1.5. That is your mistake, and learn from it.

Try and try yourself and you’ll see yourself being a master.  

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Michael Tadesse

Expertise

I can answer questions regarding Relations, linear functions and equations, Squares and square roots, Translation and Similarity, Special Properties of Right Angled Triangles, Measurement of Area and Volume, algebra. I can also answer questions related to Pre calculus, Limits and Continuity, Derivatives Applications of Derivatives, High school math in general. I can’t answer questions of the following type. Power Series, Multiple Integrals, Fourier series, Vector valued Functions.

Experience

I love mathematics as it is the mother of all sciences. I had an outstanding math results while I was in school. The tradition continues while I am in university. I have been helping elementary school Students for the past five years with mathematics problems. In fact, I have a brother who is four years younger than me I usually help him to understand what the crux of the question is before trying to solve it. He loves math very much, he is indeed one of the top scorers form his class in Mathematics. I didn’t stop helping my younger relatives after I joined the Engineering campus and I am more than ready to help anyone with my skill.

Education/Credentials
have a high school diploma with a 3.97 GPA; I also have many merit certificates granted for my outstanding results in high school math. I won a merit certificate for my participation in the Black Month Essay Contest. I took two different National Examinations in 2006 and 2007. In the former Exam I got 9As which includes Mathematics. I also have a score of 90 out of hundred in the later Examination which is the toughest known in Ethiopia. So you don’t have to worry about my ability to help my clients.

Past/Present Clients
I have never had an online client but I was helping students coming to me for assistance in Mathematics.

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