Solve the system, enter as an ordered triple. Need HELP!!

This means x = 2, y = 3 and z = 1

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Work Shown:

Double everything in the second equation to get 4x-2y+4z=6

Add this result to the first equation

The first two lines of that expression above shows us adding x+2y-4z=4 to the equation 4x-2y+4z = 6

The x terms add to x+4x = 5x

The y terms add to 2y+(-2y) = 0y

The z terms add to -4z+4z = 0z

The terms on the right hand side add to 4+6 = 10

That's how we end up with the new equation 5x+0y+0z = 10

That becomes 5x = 10 which solves to x = 2 when we divide both sides by 5.

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Use this x value in the third original equation to find z

3x-8z = -2

3(2)-8z = -2

6-8z = -2

-8z = -2-6

-8z = -8

z = -8/(-8)

z = 1

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Use the x and z values we found to find y

x+2y-4z = 4

2+2y-4(1) = 4

2+2y-4 = 4

2y-2 = 4

2y = 4+2

2y = 6

y = 6/2

y = 3

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Overall we get the solutions to be x = 2, y = 3 and z = 1

We can say the solution as an ordered triple is (x,y,z) = (2,3,1)

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

answer: hey there,

the answer you are looking for is a..

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