Solve each system by elimination
-x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20

x = -2 , y = -3 , z = 3

Step-by-step explanation:

Solve the following system:

{-x - 5 y - 5 z = 2 | (equation 1)

4 x - 5 y + 4 z = 19 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Swap equation 1 with equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

-x - 5 y - 5 z = 2 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Add 1/4 × (equation 1) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - (25 y)/4 - 4 z = 27/4 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Multiply equation 2 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Subtract 1/4 × (equation 1) from equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+(25 y)/4 - 2 z = -99/4 | (equation 3)

Multiply equation 3 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+25 y - 8 z = -99 | (equation 3)

Add equation 2 to equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y - 24 z = -72 | (equation 3)

Divide equation 3 by -24:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 16 × (equation 3) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y+0 z = 75 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 2 by -25:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 5 × (equation 2) to equation 1:

{4 x + 0 y+4 z = 4 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Subtract 4 × (equation 3) from equation 1:

{4 x+0 y+0 z = -8 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 1 by 4:

{x+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Collect results:

{x = -2 , y = -3 , z = 3

astronomers is your final answer! : )

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula