Question

What is the solution of the system of equations?

Answer 1

im working on this one now

Answer 2

x=4
y=-1
z=-3

Answer 3

Is this what you needed? or did you need the explaination as well

Answer 4

How you got it?

Answer 5

@agent0smith

Answer 6

These are not quick to solve... let's use the first and third equations to start

3x + 2y + z = 7
3x + 2y + 3z = 1

Subtract the second from the first:

3x + 2y + z = 7
-(3x + 2y + 3z = 1)
____________________
-2z = 6

now you find z = -3.

Answer 7

3x + 2y + z = 7 --->(-4)
5x + 5y + 4z = 3
-------------
-12x - 8y - 4z = -28 (result of multiplying by -4)
5x + 5y + 4z = 3
--------------add
- 7x - 3y = - 25

3x + 2y + z = 7 -->(-3)
3x + 2y + 3z = 1
----------------
-9x - 6y - 3z = -21 (result of multiplying by -3)
3x + 2y + 3z = 1
-----------------add
-6x - 4y = -20

-7x - 3y = -25 -->(-4)
-6x - 4y = -20 -->(3)
----------------
28x + 12y = 100 (result of multiplying by -4)
-18x - 12y = -60 (result of multiplying by 3)
-----------------add
10x = 40
x = 4

now sub 4 in for x
-7x - 3y = -25
-7(4) - 3y = -25
-28 - 3y = -25
-3y = -25 + 28
-3y = 3
y = -1

now sub 4 in for x and -1 in for y
3x + 2y + 3z = 1
3(4) + 2(-1) + 3z = 1
12 - 2 + 3z = 1
10+ 3z = 1
3z = 1 - 10
3z = -9
z = -3

check...
5x + 5y + 4z = 3
5(4) + 5(-1) + 4(-3) = 3
20 - 5 - 12 = 3
15 - 12 = 3
3 = 3 (correct)

x = 4, y = -1, and z = -3

Answer 8

So basically we just plug in a number into the equation to see if it comes out true? @texaschic101 and thank you so much for making it really clear.

Answer 9

to check it....you plug in the numbers that you found for x,y,and z into one of the original equations, and if it comes out equal, then you got it right. As for finding x,y,and z, that takes a little bit of time.

Answer 10

The actual solving of these equations is really tedious, as you can see from texaschic

The last part was just checking them.

Answer 11

that explains it perfectly...tedious

Answer 12

Thank you, your a math genius !lol

Answer 13

btw @texaschic101 it might've been faster had you first solved for z as i did... that took like one line of work

Answer 14

true...I should have done that :)

Answer 15

@OtonoGold After getting z = -3 plug that into two of the other equations, then solve them for x and y

Answer 16

Oh Ok, thank you. ! very helpful