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Q4.

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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

The following is a system of two linear equations in two variables.
$\{\begin{cases} x + y = 1 \\ 2 x + 2 y = 2 \end{cases}$
The graph of the first equation is the same as the graph of the second equation, so the system has ___ _solutions. We express these solutions by writing
$\begin{array}{l} x = t \\ y =__ \end{array}$
where $t$ is any real number. Some of the solutions of this system are $(1,_), (- 3,_)$ and $(5,_)$

Infinitely many solutions, $y = 1 - t$ and $(1, 0), (- 3, 4) & (5, - 4)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

In this question, we have been given a sentence.

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 complete the given sentence.

By the process of the system of equations, we will calculate the result.

Step 3. Calculation

We know that the following is a system of linear equations in two variables,

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

The graph of the first equation is the same as the second equation, so the system has infinitely many solutions. We express the solutions by writing

$\begin{array}{l} x = t \\ y = 1 - t \end{array}$

Where t is any real number. Some of the solutions of this system are $(1, 0), (- 3, 4) & (5, - 4)$

Most popular questions for Math Textbooks

Solving a General System of Equations Find x and y in

terms of a and b.

$\{\begin{cases} a x + b y = 0 \\ x + y = 1 \end{cases} (a \neq b)$

Number of Solutions

Determined Graphically Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.

$\{\begin{cases} 2 x + 6 y = 0 \\ - 3 x - 9 y = 18 \end{cases}$

John and Mary leave their house

at the same time and drive in opposite directions. John drives

at 60 mi/h and travels 35 mi farther than Mary, who

drives at 40 mi/h. Mary’s trip takes 15 min longer than

John’s. For what length of time does each of them drive?

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

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

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.

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

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