Q25. Solve each equation.3x-5x+y129z=... [FREE SOLUTION]

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.

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

– Description of step.

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

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

– 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 $(5, 3, 2)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

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

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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