solve system: 4x + 2y + z = -29, 5x - 4y - z = 1, 4x + y....

C

callie2291

New member
Joined
Jul 6, 2008
Messages
4
Solve a system of three linear equations in three variables.

4x + 2y + z = -29
5x - 4y - z = 1
4x + y + 4z = -40

Can anyone please help me out on how to do this. I'm so lost right now. Ive been at this for an hour!!
 
There are several approaches. You don't say which method you are supposed to use. Here's one way to do it.

(1) 4x + 2y + z = -29
(2) 5x - 4y - z = 1
(3) 4x + y + 4z = -40

Multiply both sides of (1) by 5.
Multiply both sides of (2) by -4
Multiply both sides of (3) by 5.

Add the new (1) to the new (2) getting an equation in y and z. Call this equation (4).
Add the new (3) to the new (2) getting another equation in y and z. Call this equation (5).
Now solve (4) and (5) for z. Plugging your value of z back into either 4 or 5, find the value of y.
Now plug the values of y and z back into one of your original equations and solve for x.
Now that you have the values of x, y and z, check your answer by plugging those values back into each of the original equations and see that they tell the truth. If they don't you have made a mistake. Start over.
 
4x + 2y + z = -29 [1]
5x - 4y - z = 1 [2]
4x + y + 4z = -40 [3]

Another way:
add equations [1] and [2] to get: 9x - 2y = -28 [4]

Multiply [2] by 4 to get: 20x - 16y - 4z = 4
add that with equation [3] to get: 24x - 15y = -36 [5]

Use [4] and [5] to get x and y
 
You must log in or register to reply here.
Top