Math Is Fun Forum

drago

Member

Registered: 2008-05-22

Posts: 1

system of equations

hi,

could someone help me solve this

solve the system of 3 equations:

x+2y=2
2x+3y-z=-9
4x+2y+5z=1

Last edited by drago (2008-05-22 20:33:16)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,341

Re: system of equations

A system of 3 equations in 3 variables is usually solved by reducing the number of variables to 2 first.

In the question you have given, x+2y=2 or x=2-2y.
Substitute this in the remaining two equations. You get
4-4y+3y-z=-9 or -y-z=-13 or y+z=13----(1)
8-8y+2y+5z=1 or -6y+5z=-7----(2)
Multiply equation(1) by 6: 6y+6z=78---(3)
Adding (1) and (3), you get z=71/11. From (1), you get  y=72/11. From x=2-2y, you get x= -122/11.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

drago

Member

Registered: 2008-05-22

Posts: 1

Re: system of equations

why did you multiply it by 6?

and could you explain this a little bit more

Last edited by drago (2008-05-22 21:51:22)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,341

Re: system of equations

The idea is to eleminate a variable.
Since equation (2) is -6y+5z=-7 and equation (1) is y+z=13,
the equation (1) is multiplied by 6 since equation (2) contains the term 6y.
By eleminationg the additional variable, the equations are solved.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.