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Q19.

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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

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.
$\{\begin{cases} - x + \frac{1}{2} y = - 5 \\ 2 x - y = 10 \end{cases}$

Hence, the system of linear equations has infinitely many solutions and the sketch of the graph is.

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-

$\{\begin{cases} - x + \frac{1}{2} y = - 5 \\ 2 x - y = 10 \end{cases}$

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 use the graph to determine whether the system has one solution, no solution, or infinitely many solutions.

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

Step 3. Calculation

Two lines indicated correspond to the two equations from the system of linear equations.

As is evident by the graphs, the two lines are overlapping and each point on either of the lines can be considered an intersection.

So, We can conclude that the system of linear equations has infinitely many solutions.

We sketch the graph,

Most popular questions for Math Textbooks

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

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

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

$\{\begin{cases} 2 x - 3 y = 9 \\ 4 x + 3 y = 9 \end{cases}$

Use a graphing device to graph both lines in the same viewing rectangle.

(Note that you must solve for y in terms of x before graphing

if you are using a graphing calculator.) Solve the system either by

zooming in and using trace or by using Intersect. Round

your answers to two decimals.

$\{\begin{cases} 2371 x - 6552 y = 13591 \\ 9851 x + 992 y = 618555 \end{cases}$

Solving a System of Equations in Three Variables

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

$\{\begin{cases} x + y + z = 4 \\ x + 3 y + 3 z = 10 \\ 2 x + y - z = 3 \end{cases}$

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

$\{\begin{array}{r} - 4 x + 12 y = & 0 \\ 12 x + 4 y = & 160 \end{array}$

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