Solve the system of linear equations by substitution.
x= 16-4y

3x+4y=8

x = - 4

y = 5

Step-by-step explanation:

x = 16 - 4y               Add 4y to both sides.

x + 4y = 16              Subtract x  from both sides

4y = 16 - x

Now look at the second equation

3x + 4y = 8              Substitute the 4y in the equation above into this equation

3x + 16 - x = 8          Combine

2x + 16 = 8               Subtract 16 from both sides

2x = 8 - 16                Combine

2x = - 8                     Divide by 2

2x / 2 = - 8/2

x = - 4

Use 3x + 4y = 8 to solve for y

Use 3(-4) + 4y = 8

-12 + 4y = 8                Add 12 to both sides

4y = 8 + 12                 Combine

4y = 20                      Divide by 4

4y/4 = 20/4            

y = 5

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