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Q13.

Expert-verified

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

Graphical Method
Two equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system.
$\{\begin{cases} 2 x + y = - 1 \\ x - 2 y = - 8 \end{cases}$

Hence, the intersection points of the graphs by solving the system are $x = - 2 & y = 3$

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-

$\{\begin{cases} 2 x + y = - 1 \\ x - 2 y = - 8 \end{cases}$

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 the intersection points of the graphs by solving the system. By the Graphical Method, we will calculate the result.

Step 3. Calculation

We multiply the first equation by $2$ and add the second equation to eliminate the $y$

$\begin{array}{l} 2 \times [2 x + y = - 1] \\ 4 x + 2 y = - 2 \\ x - 2 y = - 8 \end{array}$

Further solving,

$\begin{array}{l} (4 x + x) \\ 5 x = - 10 \\ x = - 2 \end{array}$

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

$\begin{array}{l} - 2 - 2 y = - 8 \\ 2 y = 8 - 2 \\ 2 y = 6 \\ y = 3 \end{array}$

Most popular questions for Math Textbooks

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}{4} x + \frac{1}{2} y = 5 \\ - \frac{1}{4} x - \frac{3}{2} y = 1 \end{array}

Solving a System of Equations in Three Variables

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

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

A system of two linear equations in two variables can have one solution, ______solution, or _______ ______solutions.

The sum of the digits of a two-digit

number is 7. When the digits are reversed, the number is

increased by 27. Find the number.

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.

$\{\begin{cases} - 435 x + 912 y = 0 \\ 132 x + 455 y = 994 \end{cases}$

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