-X-5y + z = 17 -5x - 5y + 5z = 5
2x + 5y- 3z=-10
Solve the systems of equations.
(x, y, z)

x = -1 , y = -4 , z = -4

Step-by-step explanation:

Solve the following system:

{-x - 5 y + z = 17 | (equation 1)

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

2 x + 5 y - 3 z = -10 | (equation 3)

Swap equation 1 with equation 2:

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

-x - 5 y + z = 17 | (equation 2)

2 x + 5 y - 3 z = -10 | (equation 3)

Subtract 1/5 × (equation 1) from equation 2:

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

0 x - 4 y+0 z = 16 | (equation 2)

2 x + 5 y - 3 z = -10 | (equation 3)

Divide equation 1 by 5:

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

0 x - 4 y+0 z = 16 | (equation 2)

2 x + 5 y - 3 z = -10 | (equation 3)

Divide equation 2 by 4:

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

0 x - y+0 z = 4 | (equation 2)

2 x + 5 y - 3 z = -10 | (equation 3)

Add 2 × (equation 1) to equation 3:

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

0 x - y+0 z = 4 | (equation 2)

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

Swap equation 2 with equation 3:

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

0 x+3 y - z = -8 | (equation 2)

0 x - y+0 z = 4 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

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

0 x+3 y - z = -8 | (equation 2)

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

Multiply equation 3 by 3:

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

0 x+3 y - z = -8 | (equation 2)

0 x+0 y - z = 4 | (equation 3)

Multiply equation 3 by -1:

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

0 x+3 y - z = -8 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Add equation 3 to equation 2:

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

0 x+3 y+0 z = -12 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Divide equation 2 by 3:

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

0 x+y+0 z = -4 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Add equation 2 to equation 1:

{-x + 0 y+z = -3 | (equation 1)

0 x+y+0 z = -4 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Subtract equation 3 from equation 1:

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

0 x+y+0 z = -4 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Multiply equation 1 by -1:

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

0 x+y+0 z = -4 | (equation 2)

0 x+0 y+z = -4 | (equation 3)

Collect results:

{x = -1 , y = -4 , z = -4

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

answer is : muchas/tipicas

have a nice day!

~recklesschicken