Question

ip. 7.2 solving systems by substitution - day 2
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1. there are x trumpet players and y saxophone players in a school’s jazz band.

the equations in the system shown here relate x and y.
a. solve the system by substitution.
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$$\begin{cases} 2x + 3y = 23 \\\\ y = 3x - 7 \\end{cases}$$

b. what does the solution mean?

Explanation:

Step1: Substitute $y$ into first equation

Substitute $y=3x-7$ into $2x+3y=23$:
$2x + 3(3x - 7) = 23$

Step2: Expand and simplify equation

$2x + 9x - 21 = 23$
$11x - 21 = 23$

Step3: Solve for $x$

$11x = 23 + 21$
$11x = 44$
$x = \frac{44}{11} = 4$

Step4: Solve for $y$

Substitute $x=4$ into $y=3x-7$:
$y = 3(4) - 7 = 12 - 7 = 5$

(Part B):
The solution means there are 4 trumpet players and 5 saxophone players in the school's jazz band, as $x$ represents trumpet players and $y$ represents saxophone players.

Answer:

(Part A):
$x=4$, $y=5$