Solve x + y - z = 0, 2x - y + z = 6, -x + y + z = 8. How do I answer as xyz?

Answer 1

well i have done is in very simple way.
x + y - z = 0...........(1)
2x - y + z = 6...........(2)
-x + y + z = 8.............(3)

add (1)(2).....then x=2
add (1(3).......theny=4
put the value of x.y in eqe...(1)
then y = 6
then xyz = 2 * 4 * 6 = 48

Answer 2

Y 2 X 6

Answer 3

x + y - z = 0,
2x - y + z = 6,
-x + y + z = 8.

We have three variables and three equations. So, we can solve for x, y and z.

From the first equation,

x + y - z = 0

x + y = z

Substituting in equation 3,

-x + y + x + y = 8

2y = 8

y = 4

Substitute the value of y and z in equation 2.

2x - 4 + x + 4 = 6

3x = 6

x = 2

z = x + y = 2 + 4 = 6

xyz = 2 x 4 x 6 = 48

Simple and fun isn't it?

Answer 4

If you sum the equation #1 and #3, you'll get 2y = 8, or y = 4. Insert that into #1 and #2, and you'll get:

2x + z = 10
x - z = -4

Now sum those up, and you'll get 3x = 6, or x = 2. From there, z is easy: z = 6.

Now I don't understand your question precisely, but if you're asking for the product of the solutions, it's 48, isn't it?

Answer 5

considering you have 2 equations and 3 unknowns, you could desire to eliminate between the variables from the two equations: enable's eliminate the variable Y from the equations by skill of multiplying the two facets of the 1st equation by skill of two and then removing the y by skill of including the two equations at the same time: First: multiply (2x +y - 5z = 0) by skill of two this provides 4x + 2y - 10z = 0 Now upload this equation with the 2nd equation and the y's cancel one yet another out: 4x + 2y - 10z = 0 3x - 2y - 4z = 0 ________________ 7x - 14z = 0 Rearranging the equation supplies: 7x = 14 z and x = 2 z Now, exchange all x's in the unique equations for z's making use of the equation (x=2z). 2x + y - 5z turns into 2(2z) + y - 5z = 0 or 4z + y - 5z = 0 Simplifying: y - z = 0 (equation a million) and y = z If y = z and x = 2z: then x could desire to equivalent 2y ( x = 2y) and the ratios could desire to be: x:y:z is two:a million:a million

Answer 6

[Adding 2 terms]

x+y-z=0
-x+y+z=8 gives 2y=8 :- y=4

Now,
y=4
So,
2x-y+z=6 becomes 2x-4+z=6 :- 2x+z=10
Similarly,
-x+y+z=8 becomes -x+4+z=8 :- -x+z=4

[Adding]
2x+z=10
-x+z= 4 gives 3x=6 :- x=2
Then,
x+y-z=0 :- 2+4-z=0 :- z=6
So,
xyz = 2*4*6 = 48 Answer

Answer 7

Set up equations
x + y - z = 0 ...... 1
2x - y + z = 6 ......2
-x + y + z = 8 ......3
Add 1 and 2
3x = 6
then x = 2
eqns become
1 ....... 2 + y - z = 0 or y - z = -2 .......4
2........ 4 - y + z = 6 or -y + z = 2 .....5
3........-2 + y + z = 8 or y + z = 10 .....6
add 5 and 6
2z = 12
then z =6
4 ...... y - 6 = -2
y = 4
(x,y,z)=(2,4,6)
Check answer by substitution
suggest you investigate matrix methods for solution.

Answer 8

say
x+y-z=0 ----(1)
2x-y+z=6-----(2)
-x+y+z=8-----(3)

from (1)
x=z-y-----(4)

put (4) in (2), (2) becomes
2(z-y)-y+z=6
2z-2y-y+z=6
2z-3y+z=6
3z-3y=6------(5)

put (4) in (3), (3) becomes
-(z-y)+y+z=8
-z+y+y+z=8 (-z & z went together zero)
2y=8 (devide by 2 both sides of equation)
y=4

put (y=4) into (5)
3z-3X4=6
3z-12=6
3z=6+12=18
z=6

from (4)
x=z-y
put (y=4 & z=6) into (4)
x=6-4
x=2

so x=2, y=4, z=6

xyz= 2X4X6= 48

the end

regards,

Answer 9

x + y - z = 0......(1)
2x - y + z = 6...(2)
-x + y + z = 8....(3)

Add (1) & (2)
3x=6
x=6/3=2

Put it in (2) & (3)
4 - y +z=6
-y+z=2 ........(4)
-2+y+z=8
y+z=10..........(5)
Add (4) & (5)
2z=12
z=12/2=6

put it in (5)
y=10-z=10-6
y=4

xyz=2*4*6=48

Answer 10

huh??????