Solve the system. x + y - 3z = -20
-3y + 2z = 5
z = 4
Enter your answer as an ordered triple.
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Step-by-step explanation:

Subtract 2z2z from both sides of the equation.

x−2y+z=1x-2y+z=1

y=5−2zy=5-2z

x+y+3z=8x+y+3z=8

Replace all occurrences of yy with 5−2z5-2z in each equation.

x−2(5−2z)+z=1x-2(5-2z)+z=1

y=5−2zy=5-2z

x+5−2z+3z=8x+5-2z+3z=8

Simplify each equation.

x−10+5z=1x-10+5z=1

y=5−2zy=5-2z

x+5+z=8x+5+z=8

Move all terms not containing xx to the right side of the equation.

x=11−5zx=11-5z

y=5−2zy=5-2z

x+5+z=8x+5+z=8

Replace all occurrences of xx in x+5+z=8x+5+z=8 with 11−5z11-5z.

x=11−5zx=11-5z

y=5−2zy=5-2z

(11−5z)+5+z=8(11-5z)+5+z=8

Simplify (11−5z)+5+z(11-5z)+5+z.

x=11−5zx=11-5z

y=5−2zy=5-2z

−4z+16

okay so 15.15 *()5: +5/6

step-by-step explanation:

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