Chapter 4: Q25. (page 157)

Solve each equation.
$[\begin{matrix} 3 x - 5 & x + y \\ 12 & 9 z \end{matrix}] = [\begin{matrix} 10 & 8 \\ 12 & 3 x + y \end{matrix}]$

Short Answer

Expert verified

The solution is $(5, 3, 2)$ .

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.

$\begin{matrix} 3 x - 5 = 10 \\ x + y = 8 \\ 3 x + y = 9 z \end{matrix}$

– Description of step.

Add 5 on both the sides of $3 x - 5 = 10$ and simplify.

$\begin{matrix} 3 x - 5 + 5 = 10 + 5 \\ 3 x = 15 \end{matrix}$

– Description of step.

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

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

– Description of step.

Substitute 5 for x into $x + y = 8$ and simplify.

$\begin{matrix} 5 + y = 8 \\ y = 3 \end{matrix}$

– Description of step.

Substitute 5 for x and 3 for y into $3 x + y = 9 z$ and simplify.

$\begin{matrix} 3 (5) + 3 = 9 z \\ 15 + 3 = 9 z \\ 18 = 9 z \end{matrix}$

– Description of step.

Divide each side of $18 = 9 z$ by 9 to find the value of z.

$\begin{matrix} \frac{18}{9} = \frac{9 z}{9} \\ z = 2 \end{matrix}$

Therefore, the solution is $(5, 3, 2)$ .

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Solve each equation.
$[\begin{matrix} 3 x - 5 & x + y \\ 12 & 9 z \end{matrix}] = [\begin{matrix} 10 & 8 \\ 12 & 3 x + y \end{matrix}]$

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.3x-5x+y129z=108123x+y

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.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Solve each equation.
$[\begin{matrix} 3 x - 5 & x + y \\ 12 & 9 z \end{matrix}] = [\begin{matrix} 10 & 8 \\ 12 & 3 x + y \end{matrix}]$