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Chapter 4: Q7. (page 156)

Solve each equation.
$[\begin{matrix} 9 & 13 \end{matrix}] = [\begin{matrix} x + 2 y & 4 x + 1 \end{matrix}]$

Short Answer

Expert verified

The solution is $(3, 3)$ .

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.

$\begin{matrix} x + 2 y = 9 \\ 4 x + 1 = 13 \end{matrix}$

02

– Description of step.

Subtract 1 from both the sides of $4 x + 1 = 13$ and simplify.

$\begin{matrix} 4 x + 1 鈭� 1 = 13 鈭� 1 \\ 4 x = 12 \end{matrix}$

03

– Description of step.

Divide each side of $4 x = 12$ by 4 to find the value of x.

\begin{matrix} \frac{4 x}{4} = \frac{12}{4} \\ x = 3 \end{matrix}

04

– Description of step.

Substitute 3 for x into $x + 2 y = 9$ and simplify.

\begin{matrix} 3 + 2 y = 9 \\ 2 y = 9 鈭� 3 \\ 2 y = 6 \end{matrix}

05

– Description of step.

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

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

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

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Most popular questions from this chapter

Solve each system of equations.

\begin{matrix} 3 a + 2 b = 27 \\ 5 a - 7 b + c = 5 \\ - 2 a + 10 b + 5 c = - 29 \end{matrix}

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

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

$4 C$

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

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

4 A + 2 B - C

For Exercises 36-39, use the following price list for one-day admissions to the community pool.

36. Write a matrix that represents the cost of admissions for residents and a matrix that represents the cost of admission for non-residents.

For exercises 30-32, use the following information. The Cookie Cutter Bakery records each type of cookie sold at three of their branch stores. Two days of sales are shown in the spreadsheets below.

31. Find the sum of the two days鈥� sales expressed as a matrix.

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