systems of equations in three variables: 2x-y+z=5 and 6x+3y-2z=10 and x-2y+3z=5?

Answer 1

2x-y+z=5
x-2y+3z=5
x=5+2y-3z

2(5+2y-3z)-y+z=5
10+4y-6z-y+z=5
4y-y-6z+z=-5
3y-5z=-5____________{1}

6(5+2y-3z)+3y-2z=10
30+12y-18z+3y-2z=10
12y+3y-18z-2z=-20
15y-20z=-20___________{2}

3y = 5z-5___________________[from {1}]


now,
15y-20z=-20
15(5z-5)-20z=-20
75z-75-20z=-20
55z=55
z=1


15y-20z=-20_________________[from{2}]
15y-20(1)=-20
15y-20=-20
15y=-1
y=-1/15

now x-2y+3z=5

x=5+2y-3z
x=5+2(-1/15)+3(1)
x=5-2/15+3
x=(75-2+45)/15
x=118/15

Answer 2

When people are telling you to use a matrix, this is what they mean:

1st you have to find the determinate.

[ 2 -1 1 ] 2 -1
D=[ 6 3 -2 ] 6 3
[ 1 -2 3 ] 1 -2

-(18) + (8) + (3) - (18)+ (2) - (-12) = -15

So your determinate is -15.

Now you have to make a matrix solving for x:

[5 -1 1] 5 -1
[10 3 -2]10 3
[5 -2 3] 5 -2

(-30) + (20) + (15) - (45) - (10) - (-20) = -30

Put your answer over the determinate and you get:
-30/-15
So.....x=2

Solve for y:
[2 5 1 ] 2 5
[6 10 -2] 6 10
[1 5 3 ] 1 5

(90) + (-20) + (10) - (60) - (-10) - (30) = 0

0/(-15) = 0

So Y= 0


Now finally for Z:

[ 2 -1 5] 2 -1
[ 6 3 10] 6 3
[ 1 -2 5] 1 -2

(-30) + (-40) + (15) - (30) - (-10) - (-60) = -15

-15 / -15 = 1

So Z= 1



your final answer is X= 2; Y= 0; Z= 1


Hope this helps some!

Answer 3

1) making x or y or z (only one) from any two chosen equations as a subject. Then substitute it into the third. Solve one variable, then the second, then the third. Im sure it'll work.

2) creating a matrix can solve this question easily.. read up some articles about matrix, it's kind of simple for this question. Something like :

2 -1 1 | 5
6 3 -2 | 10
1 -2 3 | 5

The answer should be 2,0,1

Answer 4

1st equation (Solve x):
2x - y + z = 5
2x = y - z + 5
x = 0.5y - 0.5z + 2.5

2nd equation (Solve y and substitute x);
6(0.5y - 0.5z + 2.5) + 3y - 2z = 10
3y - 3z + 15 + 3y - 2z = 10
6y - 5z = 10 - 15
6y = 5z - 5
y = 5/6z - 5/6

3rd equation (Solve z and substitute y):
(0.5y - 0.5z + 2.5) - 2y + 3z = 5
0.5y - 0.5z + 2.5 - 2y + 3z = 5
2.5z - 1.5y + 2.5 = 5
2.5z - 1.5(5/6z - 5/6) = 2.5
2.5z - 5/4z - 5/4 = 2 1/2
5/4z = 5/4
z = 1

2nd Equation (substitute z):
y = 5/6 - 5/6
y = 0

1st equation (substitute y and z):
x = 0 + 0.5 + 2.5
x = 3

Final answer: x = 3; y = 0; z = 1

This was hastily done. Please review my basic mathematical operation.

Answer 5

6x - 3y + 3z = 15
6x + 3y - 2z = 10------ADD

12x + z = 25

-4x + 2y - 2z = - 10
x - 2y + 3z = 5-----ADD

-3x + z = - 5

3x - z = 5
12x + z = 25----ADD
15x = 30
x = 2
z = 1

12 + 3y - 2 = 10
3y = 0
y = 0

x = 2 , y = 0 , z = 1

Answer 6

x=2, y=0, z=1, determinant = 15

Answer 7

Wow your smart!
But then again Im only 15.

Answer 8

Set it up in a matrix, you bum. Hint it is not a Movie.

Answer 9

Um, pi? i don't know.