The perimeter of a small rectangular garden is 14 feet. If the length is thrice the width, find the width and length of the garden.

width=1.75feet Length=5.75feet

Step-by-step explanation:

perimeter(p)=14feet

Length(L)=3xwidth(w)

L=3 x w

P=2xL+2xw

14=2xL + 2xw

Substitute L=3 x w in 14=2xL+2xw

14=2 x 3 x w +2 x w

14=6w+2w

14=8w

Divide both sides by 8

14 ➗ 8=8w ➗ 8

1.75=w

Width=1.75feet

Substitute w=1.75 in L=3 x w

L=3x1.75 L=5.25

Length=5.25feet

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

5+2x=a

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