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Chapter 4: Q22. (page 157)

Solve each equation.
$[\begin{matrix} 2 x \\ 2 x + 3 y \end{matrix}] = [\begin{matrix} y \\ 12 \end{matrix}]$

Short Answer

Expert verified

The solution is $(\frac{3}{2}, 3)$ .

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.

$\begin{matrix} 2 x = y \\ 2 x + 3 y = 12 \end{matrix}$

02

– Description of step.

Substitute $2 x$ for $y$ into $2 x + 3 y = 12$ and simplify.

$\begin{matrix} 2 x + 3 (2 x) = 12 \\ 2 x + 6 x = 12 \\ 8 x = 12 \end{matrix}$

03

– Description of step.

Divide each side of $8 x = 12$ by 8 to find the value of $x$ .

$\begin{matrix} \frac{8 x}{8} = \frac{12}{8} \\ x = \frac{3}{2} \end{matrix}$

04

– Description of step.

Substitute $\frac{3}{2}$ for $x$ into $2 x = y$ and simplify to find the value of $y$ .

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

Therefore, the solution is $(\frac{3}{2}, 3)$ .

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

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