Blake is throwing a party and needs to buy supplies to make guacamole. He bought 6 avocados and 3 limes for 11.55 at the first store. He purchased 3 more avocados and 5 more limes for 7.00 at the second store. Which system can Blake use to figure out how much he paid for each avocado and each lime? Assume that x represents the price of each avocado and y represents the cost of each lime.

Let x represents the price of each avocado and y represents the cost of each lime.

He bought 6 avocados and 3 limes for 11.55, hence:

6x + 3y = 11.55      (1)

He purchased 3 more avocados and 5 more limes for 7.00. Hence:

3x + 5y = 7            (2)

Solving equation 1 and 2 simultaneously gives:

x = $1.75, y = $0.35

The cost of each avocado is $1.75 while the cost of each lime is $0.35

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cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x