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Q48.

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Precalculus Mathematics for Calculus

Found in: Page 689

Book edition 7th Edition

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

Pages 948 pages

ISBN 9781337067508

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Short Answer

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.
$\begin{array}{l} 26 x - 10 y = - 4 \\ 0.6 x + 1.2 y = - 3 \end{array}$

Hence, the solution of the system of equations $\begin{array}{l} 26 x - 10 y = - 4 \\ 0.6 x + 1.2 y = - 3 \end{array}$ is the ordered pair $<1, 3>$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Given a system of equations $\begin{array}{l} 26 x - 10 y = - 4 \\ 0.6 x + 1.2 y = - 3 \end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$26 x - 10 y = - 4$ …….(1)

$0.6 x + 1.2 y = - 3$ …….(2)

Solving equation (1) for x,

$x = \frac{1}{26} (- 4 + 10 y)$

Step 3. Determining the angle

We are substituting equation (3) in equation (2),

$- 0.6 (\frac{- 2}{13} + \frac{5}{13} y) + 1.2 y = 3$

$\frac{6}{65} - \frac{3}{13} y + \frac{12}{10} y = 3$

Subtracting $\frac{6}{65}$ from both sides,

$\begin{array}{l} - \frac{3}{13} y + \frac{12}{10} y = 3 - \frac{6}{65} \\ \frac{- 30 y + 156 y}{130} = 3 - \frac{6}{65} \\ \frac{126 y}{130} = \frac{189}{65} \end{array}$

Multiplying both sides by $\frac{130}{126}$

$y = 3$

Now, substituting back value of y in equation (3)

$\begin{array}{l} x = \frac{- 2}{13} + \frac{5}{13} (3) \\ x = \frac{- 2}{13} + \frac{15}{13} \\ x = 1 \end{array}$

Most popular questions for Math Textbooks

Is the System of Equations Linear?

State whether the equation or system of equations is linear.

$6 x - \sqrt{3} y + \frac{1}{2} z = 0$

Solving a System of Equations in Three Variables

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

$\{\begin{cases} x - 2 y + 3 z = - 10 \\ 3 y + z = 7 \\ x + y - z = 7 \end{cases}$

Solving a System of Equations in Three Variables

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

$\{\begin{cases} x - y + z = 0 \\ y + 2 z = - 2 \\ x + y - z = 2 \end{cases}$

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.

$\begin{array}{l} \frac{3}{2} x - \frac{1}{3} y = \frac{1}{2} \\ 2 x - \frac{1}{2} y = - \frac{1}{2} \end{array}$

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.

$\begin{array}{l} 25 x - 75 y = 100 \\ - 10 x + 30 y = - 40 \end{array}$

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