Question

use a system of linear equations to solve the following problem.
a new restaurant is to contain two - seat tables and four - seat tables. fire codes limit the restaurants maximum occupancy to 62 customers. if the owners have hired enough servers to handle 18 tables of customers, how many of each kind of table should they purchase?
write a system of linear equations using the given information. choose correct answer below
a. \\( \left\\{ \

$$\begin{array} { l } { 2 x - 4 y = 62 } \\\\ { x - y = 18 } \\end{array}$$

\
ight. \\)
b. \\( \left\\{ \

$$\begin{array} { l } { 2 x + 4 y = 62 } \\\\ { x + y = 18 } \\end{array}$$

\
ight. \\)
c. \\( \left\\{ \

$$\begin{array} { l } { x + y = 62 } \\\\ { 2 x + 4 y = 18 } \\end{array}$$

\
ight. \\)
d. \\( \left\\{ \

$$\begin{array} { l } { x - y = 62 } \\\\ { 2 x - 4 y = 18 } \\end{array}$$

\
ight. \\)

Explanation:

Step1: Define variables

Let \(x\) be the number of two - seat tables and \(y\) be the number of four - seat tables.

Step2: Set up equations for the number of tables

The total number of tables is given as \(18\), so \(x + y=18\).

Step3: Set up equations for the number of customers

Each two - seat table holds \(2\) customers and each four - seat table holds \(4\) customers, and the total number of customers is \(62\). So \(2x + 4y=62\).

Answer:

B. \(

$$\begin{cases}x + y=18\\2x + 4y=62\end{cases}$$

\)