Kathryn and Pranav each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Kathryn spent $27 on 6 ft^2 of grass sod and 5 geraniums. Pranav spent $51 on 9 ft of grass sod and 11 geraniums. What is the cost of one ft^2 of grass sod and the cost of one geranium?

Step-by-step explanation:

6ft² of grass sod + 5 geraniums = $27

9 ft² of grass sod + 11 geraniums = $51

Let x represent 1ft² of grass sod.

Let y represent 1 geranium.

We have 6x + 5y = $27.

=> 1.5(6x + 5y) = 1.5 * $27, 9x + 7.5y = $40.5.

9x + 11y = $51

- (9x + 7.5y = $40.5)

=> 3.5y = $10.5, y = $3.

Therefore 6x + 5($3) = $27,

6x + $15 = $27, 6x = $12, x = $2.

Hence 1ft² of grass sod costs $2

and 1 geranium costs $3.

b. astronomers

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.