Chapter 4: Q19. (page 157)

Solve each equation.
$[\begin{matrix} 4 x - 3 & 3 y \\ 7 & 13 \end{matrix}] = [\begin{matrix} 9 & - 15 \\ 7 & 2 z + 1 \end{matrix}]$

Short Answer

Expert verified

The solution is $(3, - 5, 6)$ .

Step by step solution

– Description of step.

As the matrices are equal, the corresponding elements are equal. Write the three linear equations to show this equality.

$\begin{matrix} 4 x - 3 = 9 \\ 3 y = - 15 \\ 13 = 2 z + 1 \end{matrix}$

– Description of step.

Add 3 on both the sides of $4 x - 3 = 9$ and simplify.

$\begin{matrix} 4 x - 3 + 3 = 9 + 3 \\ 4 x = 12 \end{matrix}$

– Description of step.

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

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

– Description of step.

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

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

– Description of step.

Subtract $1$ from both the sides of $13 = 2 z + 1$ and simplify.

$\begin{matrix} 13 - 1 = 2 z + 1 - 1 \\ 12 = 2 z \end{matrix}$

– Description of step.

Divide each side of $12 = 2 z$ by 2 to find the value of z.

$\begin{matrix} \frac{12}{2} = \frac{2 z}{2} \\ z = 6 \end{matrix}$

Therefore, the solution is $(3, - 5, 6)$ .

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Solve each equation.
$[\begin{matrix} 4 x - 3 & 3 y \\ 7 & 13 \end{matrix}] = [\begin{matrix} 9 & - 15 \\ 7 & 2 z + 1 \end{matrix}]$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

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Solve each equation.4x-33y713=9-1572z+1

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

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Solve each equation.
$[\begin{matrix} 4 x - 3 & 3 y \\ 7 & 13 \end{matrix}] = [\begin{matrix} 9 & - 15 \\ 7 & 2 z + 1 \end{matrix}]$