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

it should be a and d. lmk if i'm wrong xd

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.