Question

enter the equations that represent the scenario into the graphing calculator to find how many of each type of commercial is played.
$x + y = 16$
$0.5x + y = 13$
in one hour, the radio station plays $\boldsymbol{square}$ commercials that are 30 seconds long.
in one hour, the radio station plays $\boldsymbol{square}$ commercials that are 60 seconds long.

Explanation:

Step1: Subtract the second equation from the first equation to eliminate \( y \).

\((x + y) - (0.5x + y) = 16 - 13\)
Simplify the left side: \(x + y - 0.5x - y = 0.5x\)
Simplify the right side: \(3\)
So we have \(0.5x = 3\)

Step2: Solve for \( x \).

Multiply both sides of \(0.5x = 3\) by \(2\) to get \(x = 6\)

Step3: Substitute \( x = 6 \) into the first equation \( x + y = 16 \) to find \( y \).

\(6 + y = 16\)
Subtract \(6\) from both sides: \(y = 16 - 6 = 10\)

Answer:

In one hour, the radio station plays \(\boldsymbol{6}\) commercials that are 30 seconds long.
In one hour, the radio station plays \(\boldsymbol{10}\) commercials that are 60 seconds long.