A restaurant sells basic lunches for $6 and supreme lunches for $8. You buy 12 lunches, represented by the equation x + y = 12, where x is the number of basic lunches and y is the number of supreme lunches. The equation 6x + 8y = 88 represents the total cost. How many of each type of lunch did you buy?

The number of each type of lunches he bought is as follows:

4 basic lunches and 8 supreme lunches

x = number of basic lunches

y = number of supreme lunches

You buy 12 lunches in total. Therefore,

x + y = 12

The total cost is represented as follows:

6x + 8y = 88

Let's combine the equation

x + y = 12

6x + 8y = 88

multiply the first equation by 6

6x + 6y = 72

2y  = 16

y = 16 / 2

y = 8

x + 8 = 12

x = 12 - 8

x = 4

He bought 4 basic lunches and 8 supreme lunches.

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1. Write out the equations that you have
6x + 8y = 88
x + y = 12

2. Isolate one variable is one equation. This is easiest in the second equation.
x + y = 12
-x -x
y = 12 - x

3. Plug this in for y in the other equation. Then solve that.

6x + 8 (12 - x) = 88
6x + 96 - 8x = 88
6x - 8x = -8
-2x = -8
x = 4

4. Find the other variable.

Since x = 4, that means we bought 4 basic lunches. Since we bought 12 in all, that must mean we bought 8 supreme lunches.

5. Double check by plugging in the numbers into the original equations.

6(4) + 8(8) = 88
24 + 64 = 88
88 = 88 (true)

4 + 8 = 12
12 = 12 (true)

6. Final answer
We bought 4 basic lunches and 8 supreme lunches.

Hope i can you!