What is the solution to the above system of equations?

The solution to the system of equations are  x = 7 and y = -1

2x + 3y = 11 equation 1

3x + 3y = 18 equation 2

The equations given are simultaneous equations. They would be solved using the elimination method.

In order to use the elimination method, take the following steps:

1. Subtract equation 1 from equation 2

x = 7

2. Substitute for x in equation 1

2(7) + 3y = 11

3. Expand the bracket

14 + 3y = 11

4. Combine similar terms

3y = 11 - 14

5. Add similar terms

3y = -3

6. Divide both sides of the equation by 3

y = - 1

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(x , y) = (7, - 1)

2x + 3y = 11 → (1)

3x + 3y = 18 → (2)

subtracting (1) from (2) term by term eliminates the y- term

(3x - 2x) + (3y - 3y) = (18 - 11)

x + 0 = 7 ⇒ x = 7

substitute x = 7 into either of the 2 equations and solve for y

(1) → (2 × 7) + 3y = 11

14 + 3y = 11

subtract 14 from both sides

3y = 11 - 14 = - 3

divide both sides by 3

= - 1

solution is (7 , -1)

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.'

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