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Chapter 4: Q21. (page 157)

Solve each equation.
$[\begin{matrix} 2 x + y \\ x - 3 y \end{matrix}] = [\begin{matrix} 5 \\ 13 \end{matrix}]$

Short Answer

Expert verified

The solution is $(4, - 3)$ .

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.

$\begin{matrix} 2 x + y = 5 \\ x 鈭� 3 y = 13 \end{matrix}$

02

– Description of step.

Multiply $x - 3 y = 13$ by 2 and subtract $2 x + y = 5$ from the obtained equation.

$\begin{matrix} 2 x 鈭� 6 y 鈭� (2 x + y) = 26 鈭� 5 \\ 2 x 鈭� 6 y 鈭� 2 x 鈭� y = 21 \\ 鈭� 7 y = 21 \end{matrix}$

03

– Description of step.

Divide each side of $- 7 y = 21$ by $- 7$ to find the value of $y$ .

$\begin{matrix} \frac{鈭� 7 y}{鈭� 7} = \frac{21}{鈭� 7} \\ y = 鈭� 3 \end{matrix}$

04

– Description of step.

Substitute $- 3$ for $y$ into $x - 3 y = 13$ and simplify to find the value of $x$ .

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

05

– Description of step.

Subtract 9 from both the sides of $x + 9 = 13$ and simplify.

$\begin{matrix} x + 9 鈭� 9 = 13 鈭� 9 \\ x = 4 \end{matrix}$

Therefore, the solution is $(4, - 3)$ .

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Most popular questions from this chapter

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For exercises 26 and 27, use the advertisement shown at the right.

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