solve for x y z 3x-2y+2z=1 2x+5y-5z=7 4x-3y+z=-3

Question

systems of equations containing three variables

Answer 1

3x - 2y + 2z = 1 (ill do this answer as 3 posts)

Solving for x: 3x - 2y + 2z =1  add 2y to both sides

3x + 2z = 1 + 2y  now subtract 2z from both sides

3x = 1 + 2y -2z  finally divide each side by 3

x = (1 + 2y -2z)/3 or  x= 1/3 + 2y/3 -2z/3 

Solving for y: 3x - 2y + 2z =1 subtract 3x from both sides

-2y + 2z = 1 -3x now subtract 2z from both sides

-2y = 1-3x-2z finally divide each side by -2

y = (1-3x-2z)/-2 or y= 1/-2 - 3x/-2 - 2z/-2 y= -1/2 + 3/2 + z ( the negative signs cancel out)

SOLVING for z: 3x - 2y + 2z =1 first subtract 3x from both sides

-2y + 2z = 1 - 3x next add 2y to both sides

2z = 1-3x+2y  finally divide each side by 2

z = (1-3x+2y)2 or z= 1/2 - 3x/2 + 2y/2   z=1/2-3x/2+y

 

 

Answer 2

Solving for x: 2x+5y-5z=7 first subtract 5y from each side

2x-5z=7-5y next add 5z to both sides

2x=7-5y+5z finally divide each side by 2

x=(7-5y+5z)/2

solving for y: 2x + 5y - 5z = 7 subtract 2x from each side

5y - 5z= 7-2x now add 5z to both sides

5y = (7-2x+5z) finally divide each side by 5

y = (7-2x+5z)/5 or y=7/5 -2x/5 + 5z/5   y=7/5-2x/5+z

Solving for z: 2x + 5y -5z = 7 first subtract 2x from both sides 

5y-5z=7-2x next subtract 5y

-5z = 7-2x - 5y finally divide each side by -5

z= (7-2x-5y)/-5 or z= 7/-5 - 2x/5 - 5y/5  z= -7/5 + 2x/5 + y  (negative cancel)

Answer 3

Solving for x: 4x-3y+z=-3 first add 3y to both sides

4x + z = -3 + 3y  now subtract z from both sides

4x = -3 + 3y -z  finally divide each side by 4

x= (-3 + 3y - z)/4  or x= -3/4 + 3y/4 -1z/4

Solving for y: 4x-3y+z=-3 first subtract 4x from both sides

-3y +z= -3-4x next subtract z from both sides

-3y = -3 - 4x - z finally divide each side by -3

y = (-3 - 4x - z)/-3 or -3/-3 - 4x/-3 -1z/3   y= 1 + 4x/3 + 1z/3 

Comments

I hope you don't mind my pointing out that you never solved for x, y and z.

solve for x y z 3x-2y+2z=1 2x+5y-5z=7 4x-3y+z=-3

Answer 4

2x-y+z=6

3x+2y+z=4

x-2y+3z=12

Answer 5

 

x-3y+4z=5

2x+y+z=3

4x+3y+5z=1

Answer 6

3x + y – z = 1

4x + 5y + 2z = 12

x-2y + 3z = 8

Answer 7

Use elimination to solve each equations.
1. X+y=-9
5x+2y=32

2. 3x+2y=-9
X-y=-13

3. 2x+y=3
-4x-4y=-8

4. 2x+y=0
5x+3y=2

5. 2x+3y=14
3x-4y=4

6. 3x+2y=-26
4x-5y=-4

7. 5x+2y=-3
3x+3y=9

8. 3x-6y=-3
2x+4y=30

9. Two times a number plus three times another number equals 13. The sum of the two number is 7. What are the numbers.

10. Four times a number minus twice another number is -16. The sum of thee two numbers is -1. Find the numbers

Answer 8

4x-y=1

5x+3y=14

Answer 9

cathy, it's 69

Answer 10

2x-y+2z=-7

-x+2y-4y=5

x+4y-6z=-1

Answer 11

solve for x y z 3x-2y+2z=1 2x+5y-5z=7 4x-3y+z=-3

1)  3x - 2y + 2z = 1
2)  2x + 5y - 5z = 7
3)  4x - 3y + z = -3

Multiply equation three by 2.
2 * (4x - 3y + z) = -3 * 2
4)  8x - 6y + 2z = -6

Subtract equation four from equation one.
  3x - 2y + 2z =  1
-(8x - 6y + 2z = -6)
--------------------
  -5x + 4y     = 7
5) -5x + 4y = 7

Multiply equation three by 5.
5 * (4x - 3y + z) = -3 * 5
6)  20x - 15y + 5z = -15

Add equation six to equation two.
   2x +  5y - 5z =   7
+(20x - 15y + 5z = -15)
-----------------------
  22x - 10y      =  -8
7) 22x - 10y = -8

Multiply equation seven by 2.
2 * (22x - 10y) = -8 * 2
8) 44x - 20y = -16

Multiply equation five by 5.
5 * (-5x + 4y) = 7 * 5
9) -25x + 20y = 35

Add equation eight to equation nine.
 -25x + 20y =  35
+(44x - 20y = -16)
------------------
  19x       =  19
x = 1 <<<<<<<<<<<<<<<<<

Plug the value for x into equation two.
2x + 5y - 5z = 7
2(1) + 5y - 5z = 7
2 + 5y - 5z = 7
5y - 5z = 7 - 2
10)  5y - 5z = 5

Plug the value of x into equation three.
4x - 3y + z = -3
4(1) - 3y + z = -3
4 - 3y + z = -3
-3y + z = -3 - 4
11)  -3y + z = -7

Multiply equation eleven by 5.
5 * (-3y + z) = -7 * 5
12)  -15y + 5z = -35

Add equation twelve to equation ten.
    5y - 5z =   5
+(-15y + 5z = -35)
------------------
  -10y      = -30
y = 3 <<<<<<<<<<<<<<<<<

Plug the values for x and y into equation two.
2x + 5y - 5z = 7
2(1) + 5(3) - 5z = 7
2 + 15 - 5z = 7
-5z = 7 - 2 - 15
-5z = -10
z = 2 <<<<<<<<<<<<<<<<<

To check the answers, plug the values into equation three.
4x - 3y + z = -3
4(1) - 3(3) + 2 = -3
4 - 9 + 2 = -3
6 - 9 = -3
-3 = -3

Use equation one as well.
3x - 2y + 2z = 1
3(1) - 2(3) + 2(2) = 1
3 - 6 + 4 = 1
7 - 6 = 1
1 = 1