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Chapter 4: Q20. (page 157)

Solve each equation.
$[\begin{matrix} x + 3 y \\ 3 x + y \end{matrix}] = [\begin{matrix} - 13 \\ 1 \end{matrix}]$

Short Answer

Expert verified

The solution is $(2, - 5)$ .

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.

$\begin{matrix} x + 3 y = 鈭� 13 \\ 3 x + y = 1 \end{matrix}$

02

– Description of step.

Multiply $3 x + y = 1$ by 3 and subtract $x + 3 y = - 13$ from the obtained equation.

$\begin{matrix} 9 x + 3 y 鈭� (x + 3 y) = 3 鈭� (鈭� 13) \\ 9 x + 3 y 鈭� x 鈭� 3 y = 16 \\ 8 x = 16 \end{matrix}$

03

– Description of step.

Divide each side of $8 x = 16$ by 8 to find the value of $x$ .

$\begin{matrix} \frac{8 x}{8} = \frac{16}{8} \\ x = 2 \end{matrix}$

04

– Description of step.

Substitute 2 for $x$ into $3 x + y = 1$ and simplify to find the value of $y$ .

$\begin{matrix} 3 (2) + y = 1 \\ 6 + y = 1 \end{matrix}$

05

– Description of step.

Subtract 6 from both the sides of $6 + y = 1$ and simplify.

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

Therefore, the solution is $(2, - 5)$ .

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Most popular questions from this chapter

State the dimensions of each matrix.

14. $[\begin{matrix} 17 & 鈭� 2 & 8 & 鈭� 9 & 6 \\ 5 & 11 & 20 & 鈭� 1 & 4 \end{matrix}]$

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

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

Determine whether each matrix product is defined. If so, state the dimensions of the product. $M_{4 脳 3} 鈰� N_{4 脳 3}$

Give an example of two matrices whose sum is zero matrix.

Solve each equation.

$[\begin{matrix} 2 x & 3 & 3 z \end{matrix}] = [\begin{matrix} 5 & 3 y & 9 \end{matrix}]$

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