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Q12.

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Precalculus Mathematics for Calculus

Found in: Page 688

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Elimination Method
Use the elimination method to find all solutions of the system of equations.
$\{\begin{cases} 2 x - 5 y = - 18 \\ 3 x + 4 y = 19 \end{cases}$

Hence, all solutions of the system of equations are $x = 1 & y = 4$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

We are given the system of linear equations that is-

$\{\begin{cases} 2 x - 5 y = - 18 \\ 3 x + 4 y = 19 \end{cases}$

Step 2. Concept used

The system of linear equations is the collection of one or more linear equations involving the same set of variables.

We need to find all solutions to the system of equations.

By the Elimination Method, we will calculate the result.

Step 3. Calculation

We multiply the first equation by $2$ and add the second equation to it to eliminate the x term.

$\begin{array}{l} 3 \times [2 x - 5 y = - 18] \\ 6 x - 15 y = - 54 \\ 2 \times 3 x + 4 y = 19 \\ 6 x + 8 y = 38 \end{array}$

Further solving,

$\begin{array}{l} (6 x - 6 x) + (- 15 y - 8 y) = - 54 - 38 \\ - 23 y = - 92 \\ y = 4 \end{array}$

We substitute the value of y in any of the original equations to get back the value of x

$\begin{array}{l} 3 x + 4 \times 4 = 19 \\ 3 x + 16 = 19 \\ 3 x = 3 \\ x = 1 \end{array}$

Most popular questions for Math Textbooks

Solving a System of Equations in Three Variables

Find the complete solution of the linear system, or show that it is inconsistent.

$\{\begin{cases} x - 4 z = 1 \\ 2 x - y - 6 z = 4 \\ 2 x + 3 y - 2 z = 8 \end{cases}$

Eliminating a Variable

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.

$\{\begin{cases} 2 x + y - 3 z = 5 \\ 2 x + 3 y + z = 13 \\ 6 x - 5 y - z = 7 \end{cases}$

Eliminate the $x$ -term from the third equation.

Solving a System of Equations

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 6

$\{\begin{cases} x + y = 7 \\ 2 x - 3 y = - 1 \end{cases}$

These exercises refer to the following system:

$\{\begin{cases} x - y + z = 2 \\ - x + 2 y + z = - 3 \\ 3 x + y - 2 z = 2 \end{cases}$

To eliminate x from the third equation, we add_______ times the first equation to the third equation. The third equation becomes _______ $=$ ________

A biologist has two brine solutions, one

containing 5% salt and another containing 20% salt. How

many milliliters of each solution should she mix to obtain

1 L of a solution that contains 14% salt?

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