Question

1. anna wants to sell toy cars at a craft fair for $12 each. the materials for each car cost $3.50, and the table rental at the fair costs $34 for the day. how many cars must anna sell for her revenue to equal her expenses? a 3 c 4 b 10 d 3.5 5. what is the solution of the system of equations? 2x + 5y = 14 x + 3y = 16 (\boxed{ }, \boxed{ }) 6. which has the same solution as the system of equations shown? 3x + 2y = -5 2x + 3y = 5 a 6x + 4y = -5 6x + 9y = 5 b 9x + 6y = -15 4x + 6y = 10 c 6x + 4y = -10 -6x + 9y = 15 d 6x + 4y = -10 6x + 9y = 5 7. what is the solution of the system of equations? 5x + 2y = 9 4x - 3y = 44 (\boxed{ }, \boxed{ })

Explanation:

Question 4

Step1: Define variables

Let \( x \) be the number of toy cars sold. Revenue \( R = 12x \), Expenses \( E = 3.5x + 34 \).

Step2: Set revenue = expenses

\( 12x = 3.5x + 34 \)

Step3: Solve for \( x \)

\( 12x - 3.5x = 34 \)
\( 8.5x = 34 \)
\( x = \frac{34}{8.5} = 4 \)

Step1: Solve the second equation for \( x \)

From \( x + 3y = 16 \), we get \( x = 16 - 3y \).

Step2: Substitute \( x \) into the first equation

Substitute \( x = 16 - 3y \) into \( 2x + 5y = 14 \):
\( 2(16 - 3y) + 5y = 14 \)
\( 32 - 6y + 5y = 14 \)
\( 32 - y = 14 \)
\( -y = 14 - 32 \)
\( -y = -18 \)
\( y = 18 \)

Step3: Find \( x \)

Substitute \( y = 18 \) into \( x = 16 - 3y \):
\( x = 16 - 3(18) = 16 - 54 = -38 \)

Step1: Analyze the original system

Original system: \( 3x + 2y = -5 \) and \( 2x + 3y = 5 \). We can multiply equations to eliminate variables. For option B:
First equation of B: \( 9x + 6y = -15 \) (multiply original first equation by 3: \( 3(3x + 2y) = 3(-5) \Rightarrow 9x + 6y = -15 \))
Second equation of B: \( 4x + 6y = 10 \) (multiply original second equation by 2: \( 2(2x + 3y) = 2(5) \Rightarrow 4x + 6y = 10 \))
This is equivalent to the original system (scaled equations, same solution).

Step2: Check other options

Option A: First equation not scaled correctly. Option C: Sign error in second equation. Option D: Second equation not scaled correctly.

Answer:

C 4

Question 5