Question

1. $y = -3x + 4$

$y = -8x + 14$

1. $y = -8x - 24$

$-4x + 3y = 12$

1. $y = -6$

$4x - 4y = 4$

1. $y = 3x - 15$

$-4x + 4y = -4$

1. wilburs school is selling tickets to a spring musical. on the first day of ticket sales the school sold 12 adult tickets and 12 student tickets for a total of $300. the school took in $217 on the second day by selling 4 adult tickets and 13 student tickets. find the price of an adult ticket and the price of a student ticket.

Explanation:

Problem 13

Step1: Set equations equal

$-3x + 4 = -8x + 14$

Step2: Solve for $x$

$$\begin{align*} -3x + 8x &= 14 - 4 \\ 5x &= 10 \\ x &= 2 \end{align*}$$

Step3: Substitute $x=2$ to find $y$

$y = -3(2) + 4 = -6 + 4 = -2$

Step1: Substitute $y=-8x-24$ into second equation

$-4x + 3(-8x - 24) = 12$

Step2: Simplify and solve for $x$

$$\begin{align*} -4x -24x -72 &= 12 \\ -28x &= 12 + 72 \\ -28x &= 84 \\ x &= -3 \end{align*}$$

Step3: Substitute $x=-3$ to find $y$

$y = -8(-3) -24 = 24 -24 = 0$

Step1: Substitute $y=-6$ into second equation

$4x - 4(-6) = 4$

Step2: Simplify and solve for $x$

$$\begin{align*} 4x + 24 &= 4 \\ 4x &= 4 - 24 \\ 4x &= -20 \\ x &= -5 \end{align*}$$

Answer:

$x=2,\ y=-2$

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Problem 14