Solve.
-The equation that represents the proper traffic control and emergency vehicle response availability in a small city is

2 \mathrm { P } + 3 \mathrm {~F} \leq 23

, where

\mathrm { P }

is the number of police cars on active duty and

\mathrm { F }

is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation

4 \mathrm { P } + 2 \mathrm {~F} \leq 34

is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so

P \geq 0

and

F \geq 0

. Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for

\mathrm { P }

and the vertical axis for

\mathrm { F }

. If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?
$Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2 \mathrm { P } + 3 \mathrm {~F} \leq 23 , where \mathrm { P } is the number of police cars on active duty and \mathrm { F } is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4 \mathrm { P } + 2 \mathrm {~F} \leq 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P \geq 0 and F \geq 0 . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for \mathrm { P } and the vertical axis for \mathrm { F } . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied? A) B) C) D)$

A) $Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2 \mathrm { P } + 3 \mathrm {~F} \leq 23 , where \mathrm { P } is the number of police cars on active duty and \mathrm { F } is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4 \mathrm { P } + 2 \mathrm {~F} \leq 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P \geq 0 and F \geq 0 . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for \mathrm { P } and the vertical axis for \mathrm { F } . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied? A) B) C) D)$
B) $Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2 \mathrm { P } + 3 \mathrm {~F} \leq 23 , where \mathrm { P } is the number of police cars on active duty and \mathrm { F } is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4 \mathrm { P } + 2 \mathrm {~F} \leq 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P \geq 0 and F \geq 0 . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for \mathrm { P } and the vertical axis for \mathrm { F } . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied? A) B) C) D)$
C) $Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2 \mathrm { P } + 3 \mathrm {~F} \leq 23 , where \mathrm { P } is the number of police cars on active duty and \mathrm { F } is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4 \mathrm { P } + 2 \mathrm {~F} \leq 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P \geq 0 and F \geq 0 . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for \mathrm { P } and the vertical axis for \mathrm { F } . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied? A) B) C) D)$
D) $Solve. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2 \mathrm { P } + 3 \mathrm {~F} \leq 23 , where \mathrm { P } is the number of police cars on active duty and \mathrm { F } is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4 \mathrm { P } + 2 \mathrm {~F} \leq 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P \geq 0 and F \geq 0 . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for \mathrm { P } and the vertical axis for \mathrm { F } . If 5 police cars are on active duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied? A) B) C) D)$

If Possible, Solve the System of Equations 4x+52y=303x+12y=17\begin{array} { l } 4 x + \frac { 5 } { 2 } y = 30 \\3 x + \frac { 1 } { 2 } y = 17\end{array}4x+25​y=303x+21​y=17​

Multiple Choice

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If Possible, Solve the System of Equations $\begin{array} { l } 4 x + \frac { 5 } { 2 } y = 30 \\3 x + \frac { 1 } { 2 } y = 17\end{array}$

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