Question

A caterer is making cookie trays for upcoming holiday parties.

Write an equation for trays made in the morning: 3x + 2y = 129
Write an equation for trays made in the afternoon: 3x + y = 87
What is the solution to the system of equations above?
a) x = 30, y = 29
b) x = 29, y = 30
c) x = 32, y = 25
d) x = 25, y = 32

Answer 1

The system of linear equations given is solved using the elimination method, yielding a solution of x = 15 and y = 42, which does not match any of the provided options.

Step-by-step explanation:

We are given two linear equations:

1. 3x + 2y = 129 for the morning trays.
2. 3x + y = 87 for the afternoon trays.

To find the solution to this system of equations, we can use either substitution or elimination. Here, we'll use the elimination method. Subtracting the second equation from the first eliminates the variable x:

3x + 2y - (3x + y) = 129 - 87

Which simplifies to:

y = 42

Now we substitute y back into one of the original equations, let's choose the second one:

3x + y = 87

3x + 42 = 87

Subtracting 42 from both sides, we get:

3x = 45

Dividing by 3:

x = 15

Therefore, the solution is x = 15, y = 42, which is not one of the provided options, suggesting there might be a mistake in the question or the options given.