Answer
Hotel cost per day: $\$80$
Car cost per day: $\$60$
Work Step by Step
Let's note:
$h$=the dayly cost of the hotel
$c$=the dayly cost of the car
We can write the system of equations:
$\begin{cases}
3h+2c=360\\
4h+3c=500
\end{cases}$
Use the addition method: multiply Equation 1 by -3, Equation 2 by 2 and them to eliminate $c$ and determine $h$:
$\begin{cases}
-3(3h+2c)=-3(360)\\
2(4h+3c)=2(500)
\end{cases}$
$\begin{cases}
-9h-6c=-1080\\
8h+6c=1000
\end{cases}$
$-9h-6c+8h+6c=-1080+1000$
$-h=-80$
$h=80$
Substitute the value of $h$ in Equation 1 to find $c$:
$3h+2c=360$
$3(80)+2c=360$
$240+2c=360$
$2c=360-240$
$2c=120$
$c=60$
The system's solution is:
$h=80$
$c=60$
