Chapter 9.6, Problem 19IP

a.

To determine

Tofind: the system of equations to represents the solution.

Answer to Problem 19IP

The system of equation to represents the solution is $2x+y=8\text{ and }3x+2y=13$ .

Explanation of Solution

Given information:

The cost of $2$ bagels and $1$ can of orange juice is $\$8$ . The cost of $3$ bagels and $2$ cans of orange juice is $\$13$ .

Calculation: to find the system of equation,

Let $x$ represents the cost of bagels and $y$ represents the cost of cans.

Since, The cost of $2$ bagels and $1$ can of orange juice is $\$8$ ,

  $2x+y=8$

The cost of $3$ bagels and $2$ cans of orange juice is $\$13$ ,

  $3x+2y=13$

Thus, the system of equations is $2x+y=8\text{ and }3x+2y=13$ .

b.

To determine

To find: the solution of system of equations.

Answer to Problem 19IP

The solution of system of equations is $\left(3,2\right)$ .

Explanation of Solution

Given information:

The system of equations is $2x+y=8\text{ and }3x+2y=13$ .

Calculation: to find the solution, first multiply the first equation by two and then simplify,

  $\begin{array}{l}2x+y=8\text{ [eq}\text{.1]}\\ 3x+2y=13\text{ [eq}\text{. 2]}\\ 4x+2y=16\text{ [multiply eq}\text{.1 by 2] [eq}\text{.3]}\\ x=3\text{ [ eq}\text{.3 }-\text{ eq}\text{.1]}\\ 2\left(3\right)+y=8\text{ [substitute in eq}\text{.1]}\\ y=2\text{ [simplify]}\end{array}$

Thus, the solutions of system of equations is $\left(3,2\right)$ .

The solutions means is that the cost of bagels is $\$3$ and the cost of cans is $\$2$ .