Linear equations involving 3 variables

[Chase2001]

Hello everyone. My name is Chase and I'm here to get some help with my math. I have the following problem. Solve the following system of linear equations:

 

1) 2x-3y+z=0

2) x+y+z=1

3) x-2y-4z=2

 

From what I have learnt in my book. I can take two of the equations and get rid of a variable, then I need to take two more equations and get rid of the same variable. This is what I have so far.

 

I take equation 1 and 3 and multiply the first by 4

 

1) 8x-12y+4z=0

3) x-2y-4z=8

 

This gives me 9x+14y=9

 

Now I take equations 2 and 3 and multiply equation 2 by 4.

 

2) 4x+4y+4z=4

3) x-2y-4z=2

 

This gives me 5x+2y=6. Now if I understand I now need to take these 2 new equations and solve for x or y? I guess i'll multiply the second equation by 7 to get rid of the y. Then i'll change the signs to make the subtraction

 

 

9x+14y=9

-35x-14y=-42

 

This gives me

 

-26x=-33 which is x=33/26 so now I have found the value of x which I can plug back into the equations to find the other variables but I'm not sure if this is even correct? It seems very long just to get the answers.

Edited February 2, 2014 by Chase2001

[timo]

There is at least one mistake in the calculations you made (I stopped reading at some point). But the approach is correct.

[Chase2001]

There is at least one mistake in the calculations you made (I stopped reading at some point). But the approach is correct.

 

Oh yeh I see my error but the approach is ok which is what I wanted to know. It just gets a bit confusing because I end up with so many equations on my page lol

[studiot]

A little judicious examination of the coefficients in the equations can reduce the work and increase the accuracy of this method.

 

[Chase2001]

A little judicious examination of the coefficients in the equations can reduce the work and increase the accuracy of this method.

 

equ1.jpg

 

Thanks this makes it a bit clearer. Much faster than my method. Direct substituation works for all linear equations right?

[studiot]

Well I left the process of combining equations after I had eliminated one variabele (x).

 

That generated two equations in two unknowns, y and z.

 

a simple method to reduce that to one equation in one variable would be to eliminate (z) by multiplying the second of these by 5 and subtracting from the first.

 

But since this is homework help I left that for you.

 

But do come back for more help as you progress

 

Picking out the right equations to combine is really just a matter of practise.