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Chapter 4: Q18. (page 157)

Solve each equation.
$[\begin{matrix} 4 x \\ 5 \end{matrix}] = [\begin{matrix} 15 + x \\ 2 y - 1 \end{matrix}]$

Short Answer

Expert verified

The solution is $(5, 3)$ .

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.

$\begin{matrix} 4 x = 15 + x \\ 5 = 2 y 鈭� 1 \end{matrix}$

02

– Description of step.

Add 1 on both the sides of $5 = 2 y - 1$ and simplify.

$\begin{matrix} 5 + 1 = 2 y 鈭� 1 + 1 \\ 6 = 2 y \end{matrix}$

03

– Description of step.

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

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

04

– Description of step.

Subtract $x$ from both the sides of $4 x = 15 + x$ and simplify.

$\begin{matrix} 4 x 鈭� x = 15 + x 鈭� x \\ 3 x = 15 \end{matrix}$

05

– Description of step.

Divide each side of $3 x = 15$ by 3 to find the value of $x$ .

$\begin{matrix} \frac{3 x}{3} = \frac{15}{3} \\ x = 5 \end{matrix}$

Therefore, the solution is $(5, 3)$ .

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Most popular questions from this chapter

28. Write a $4 脳 4$ matrix to organize this information.

Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.

18. $5 [\begin{matrix} 0 & 鈭� 1 & 7 & 2 \end{matrix}] + 3 [\begin{matrix} 5 & 鈭� 8 & 10 & 鈭� 4 \end{matrix}]$

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

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

25. $D - B$

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

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

$A + B + C$

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?

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