Write a system of equations to describe the situation below.solve using any method, and fill in the blanks. Pete likes to make desserts for bake sales . Last month, he made 1 batch of brownies and 3 batches of cookies, which called for 15 eggs total. The month before, he baked 2 batches of brownies and 3 batches of cookies, which required a total of 18 eggs. How many eggs did Pete use for a batch of each dessert? Pete uses square eggs to make a batch of brownies and square eggs to make a batch of cookies.

Let's denote the number of eggs needed for a batch of brownies as $$b$$ and the number of eggs needed for a batch of cookies as $$c$$ . We can set up the following system of equations based on the information provided:

1. $$b + 3c = 15$$ (from the first month's data)
2. $$2b + 3c = 18$$ (from the previous month's data)

We can solve this system of equations using the substitution or elimination method. Let's use the elimination method:

First, we can multiply the first equation by 2 to make the coefficients of $$b$$ in both equations the same:

$$2b + 6c = 30$$

Now we have the system of equations:

$$2b + 6c = 30$$
$$2b + 3c = 18$$

Next, we can subtract the second equation from the first equation to eliminate $$b$$ :

$$(2b + 6c) - (2b + 3c) = 30 - 18$$
$$3c = 12$$

Dividing both sides by 3, we get:

$$c = 4$$

Now that we have the value of $$c$$ , we can substitute it back into one of the original equations to solve for $$b$$ . Let's use the first equation:

$$b + 3(4) = 15$$
$$b + 12 = 15$$

Subtracting 12 from both sides, we get:

$$b = 3$$

Therefore, Pete uses $$\boxed{3}$$ eggs to make a batch of brownies and $$\boxed{4}$$ eggs to make a batch of cookies.