# Algebra

posted by .

solving linear equations with 3 variables

1) x+y=1300
2) x+2z=1400
3) x+y+z=1600

this one should be so easy but i don't get which equation i should pick first?!

• Algebra -

It does not matter which you pick.
However since there is one times x in each it is easy to eliminate x.

x + y = 1300
x + 2z = 1400
-------------- subtract
y - 2 z = -100

then do the first and the third for example
x + y = 1300
x + y + z = 1600
---------------------
subtract
-z = -300
or z = 300
That was just lucky that there is no y term
If there were we would use the two equations left with y and z to get rid of one or the other.
now with z = 300 go back and use the one in x and z to get x
x + 2(300) = 1400
I think you can take it from there.

• Algebra -

You subtract? arent you supposed to add?

• Algebra -

A much easier way to do this would be:
1) x+y=1300
2) x+2z=1400
3) x+y+z=1600
Look at 1 and 2. Since x+y=1300 and x+y+z=1600, z obviously equals 300. Now substitute that back in #2.
x+2(300)=1400, x+600=1400, x=800.
Now substitute x and z back in #3.
x+y+z=1600, 800+y+300=1600, 1100+y=1600, y=500

• Algebra -

THanks Damon and Jen! (especially Jen ;)

## Similar Questions

1. ### math

can someone correct these for me. 8x –4y = 16 y = 2x –4 My answer: This problem does not have a unique solution. This problem therefore is consistent and dependent These equations are the same. If you solve the first one for y, …
2. ### Algebra

It does, thanks. I'm currently working on solving algebraic equations with two variables (Example: 3x+4y=9). The computer lesson has taught me nothing but to solve the equation by trial and error -- selecting the proper ordered pair …
3. ### math

Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing …
4. ### algebra2

solve the equation: First: x + 3y = 5 Second: 3x - y = 5 should i use substitution or add them?
5. ### quick question regarding equations

I know there are methods out there but what do you think is the best or easiest method(s) of solving a system of equations. Depends on the coefficients of the equation. If in one of the equations I can solve for one of the variables …
6. ### Algebra 2

Solving systems of linear equations in three variables. Ok so i don't really totally get these problems. Can you help me solve this one?
7. ### Algebra SOLVING LINEAR EQUATIONS AND INEQUALITIES

Please help Im am Grade 5 and my teacher is letting me do this. 1. Solve the solution by using elimination and substitution 3/x - 2/y = 14 6/x + 3/y = 7 2. Solve by eliminating x (this is solving 3 linear equations) then substitute …
8. ### Algebra I DONT KNOW HOW TO DO 3 VARIABLES

Solving Linear Equations and Inequalities Solve by eliminating x (this is solving 3 linear equations) then substitute to the other two equation x + y + 5z =2 (1) 4x - 3y + 5z =3 (2) 3x - 2y + 5z=1 (3) my teacher gave me the answer …
9. ### Algebra

Solving Linear Equations and Inequalities Solve by eliminating x (this is solving 3 linear equations) then substitute to the other two equation x + y + 5z =2 (1) 4x - 3y + 5z =3 (2) 3x - 2y + 5z=1 (3) my teacher gave me the answer …
10. ### Math

PLEASE CHACK MY ANSWER!!! Discussion for Applications of Linear Systems When solving a system of equations, how do you determine which method to use?

More Similar Questions