Solving Simultaneous Equations: Step-by-Step Guide and Explanation

AI Thread Summary
To solve the simultaneous equations 2a+b+2c=z, a+2b+c=4, and a+b+2c=3, one can substitute equations into each other while treating z as a constant. Initially, attempts to eliminate variables by multiplying equations were made, but a more effective approach involves substitution to reduce the number of variables. By canceling out one variable at a time, such as 'a', and simplifying the equations, two equations with two unknowns can be derived. This method allows for expressing a, b, and c in terms of z and a constant. The discussion concludes with the user successfully finding the solution after applying the suggested substitution technique.
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Homework Statement


Find a,b,c,z
2a+b+2c=z
a+2b+c=4
a+b+2c=3

2. The attempt at a solution
Ok so I've tried multiplying all lines by 2 so you may possibly cancel out 2a, but not sure where to go after i multiplied everything.

Then i tried to just cancel one equation and then another one e.g

4a+5b+4c=10
4a+4b+8c=12

B-4c=-2

But not sure.

I would really like an explanation on how to actually do it rather than the answer.
 
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the question has given 4 variables and only 3 equations so you can not find a,b,c,z what you may be able to do is find a,b,c in terms of z and a constant.

to do this continue wih the subsitition of one equation into another treating z as a constant

not sure how you got 4a+5b+4c=10, 4a+4b+8c=12

but try subsituting
a+2b+c=4
a+b+2c=3 canceling the 'a'
and do the same with
2a+b+2c=z
a+2b+c=4
then you will have 2 equations and two unkowns, I'm sure you can see where to go with that
 
Ok thanks for the help I've figured it out. i appreciate the help :D
 

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