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Chapter 4: Q36. (page 158)

What is the value of $y$ if $[\begin{matrix} 3 x \\ y + 5 \end{matrix}] = [\begin{matrix} 9 + y \\ x \end{matrix}]$ ?
A. 2 B. 4 C. $- 3$ D. localid="1648213664321" $- 1$

Short Answer

Expert verified

The value of y is $- 3$ .

Step by step solution

01

– Description of step.

As the matrices are equal, the corresponding elements are equal. Write the two linear equations to show this equality.

\begin{matrix} 3 x = 9 + y \\ y + 5 = x \end{matrix}

02

– Description of step.

Substitute $y + 5$ for x into $3 x = 9 + y$ and simplify.

\begin{matrix} 3 (y + 5) = 9 + y \\ 3 y + 15 = 9 + y \\ 3 y 鈭� y = 9 鈭� 15 \\ 2 y = 鈭� 6 \end{matrix}

03

– Description of step.

Divide each side of $2 y = - 6$ by 2 to find the value of $y$ .

\begin{matrix} \frac{2 y}{2} = \frac{鈭� 6}{2} \\ y = 鈭� 3 \end{matrix}

Therefore, option C is the correct answer.

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Most popular questions from this chapter

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ 鈭� 1 & 6 \\ 3 & 鈭� 9 \end{matrix}], 鈥夆赌� B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], 鈥夆赌� C = [\begin{matrix} 0 & 4 \\ 鈭� 2 & 5 \\ 7 & 鈭� 1 \end{matrix}], 鈥夆赌� D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ 鈭� 3 & 0 \end{matrix}]$

$4 C$

For exercise 43-45, use the following information.

The parking garage at Burrough鈥檚 Department store charges $ $1.50$ for each hour or fraction of an hour for parking.

43. Graph the function.

For Exercises 33-35, use the table that shows the total number of deaths due to severe weather.

35. What type of severe weather accounted for most deaths each year?

Solve each equation.

[\begin{matrix} 2 x + y \\ x - 3 y \end{matrix}] = [\begin{matrix} 5 \\ 13 \end{matrix}]

For exercises 30 and 31, use the costs for an overnight stay at a hotel that are given below.

Single room: $\(60$ weekday; $\) 79$ weekend

Double room: $\(70$ weekday; $\) 89$ weekend

Suite: $\(75$ weekday; $\) 95$ weekend

30. Write a $2 脳 3$ matrix that represents the cost of each room.

See all solutions

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