Chapter 6: Q18. (page 361)

Use elimination to solve each system of equations.
$\begin{matrix} 9 x - 24 y = - 6 \\ 3 x + 4 y = 10 \end{matrix}$

Short Answer

Expert verified

The required solution is represented by $x = 2$ and . $y = 1$

Step by step solution

Step 1. Number the provided equations.

Make consideration that,

$9 x - 24 y = - 6 ...... (1) 3 x + 4 y = 10 ...... (2)$

Step 2. Make a third equation.

Take equation (2) and perform multiplication between it and 3.

$3 (3 x + 4 y) = 3 (10) 9 x + 12 y = 30 ...... (3)$

Step 3. Perform subtraction of equation (3) from the equation (3) to get the value of y after it use the obtained value to get the value of x.

Perform subtraction of equation (1) from the equation (3) to extract the value of y.

$(9 x + 12 y) - (9 x - 24 y) = 30 - (- 6) 9 x + 12 y - 9 x + 24 y = 30 + 6 36 y = 36 y = \frac{36}{36} y = 1$

Use the obtained value of y into equation (1) to get the value of x.

$9 x - 24 (1) = - 6 9 x - 24 = - 6 9 x = - 6 + 24 9 x = 18 x = \frac{18}{9} x = 2$

Step 4. Write the conclusion.

The obtained value of x and y represents the required solution that is $x = 2$ and $y = 1$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Monarch Middle School
Bake sale
Pies	$\) 10$
Cakes	$$ 8$

Use elimination to solve each system of equations.
$\begin{matrix} 9 x - 24 y = - 6 \\ 3 x + 4 y = 10 \end{matrix}$

Short Answer

Step by step solution

Step 1. Number the provided equations.

Step 2. Make a third equation.

Step 3. Perform subtraction of equation (3) from the equation (3) to get the value of y after it use the obtained value to get the value of x.

Step 4. Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Mechanics Maths

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use elimination to solve each system of equations. 9x−24y=−63x+4y=10

Short Answer

Step by step solution

Step 1. Number the provided equations.

Step 2. Make a third equation.

Step 3. Perform subtraction of equation (3) from the equation (3) to get the value of y after it use the obtained value to get the value of x.

Step 4. Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Mechanics Maths

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use elimination to solve each system of equations.
$\begin{matrix} 9 x - 24 y = - 6 \\ 3 x + 4 y = 10 \end{matrix}$