How would you go about finding the solution to this system of three equations in 3 variables?

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- anonymous

How would you go about finding the solution to this system of three equations in 3 variables?

- chestercat

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- anonymous

can i see those three equations
it might help

- anonymous

2x - y + z = 7
x + 2y - 5z = -1
x - y = 6

- anonymous

you can probably use the last equation and make x = y + 6
substitute that value into the first or second equation and find y = and then substitue that back into the last equation to get x =
i did this 3 years ago in my freshman year but you can try it. If you want i will try to figure this question out and tel you the answer 10 minutes from now? :O

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- anonymous

its okay, you don't have to work it out hun (:

- anonymous

just to be on the safe side :)

- anonymous

Here it goes:
Label all the equations by numbers...gonna be useful
2x - y + x =7 (1)
x + 2y - 5z = -1 (2)
x - y = 6 (3)
find a equation with a coefficient you can eliminate using another equation
I chose (1) and (2)
Make one variable have the same coefficient
Since the third equation consist only of x and y --> we need to eliminate z in this one
2x - y + z = 7 (1) x 5
x + 2y -5z = -1 (2)
10x - 5y + 5z = 35
+ x + 2y -5z = -1
-------------------
11x - 3y = 34
Now that you made an equation consisting of x and y: solve for one variable using substitution or elimination
rearrange (3)
x - y = 6
x = y + 6
substitute x = y - 6 into 11x - 3y = 34
11x - 3y = 34
11(y + 6) - 3y = 34
11y + 66 - 3y = 34 * combine the like terms and move 66 to the right side
11y - 3y = 34 - 66
8y = -32 * Divide both sides by 8
y = -4
one variable down two more to go
substitute y = -4 into (3). Make sure you use the original equation and not the re arranged one :D
x - y = 6
x - (-4) = 6
x + 4 = 6 * Move 4 over to the other side
x = 6 - 4
x = 2
Alright now you got two variables and you need the last one :D
substitute x = 2 and y = -4 into equation (2)
2x - y + z = 7 (2)
2(2) - (-4) + z = 7
4 + 4 + z = 7
8 + z = 7
z = 7 - 8
z = -1
You got all three variables. Write your therefore statement.
Therefore, x = 2, y = 4 and z = -1
Moral of the question: the order matters

- anonymous

thank you (:

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