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Q6.

Expert-verified

Precalculus Mathematics for Calculus

Found in: Page 697

Book edition 7th Edition

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

Pages 948 pages

ISBN 9781337067508

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Short Answer

Is the System of Equations Linear?
State whether the equation or system of equations is linear.
$\{\begin{cases} x - 2 y + 3 z = 10 \\ 2 x + 5 y = 2 \\ y + 2 z = 4 \end{cases}$

Hence all the equations in the system of equations is linear:

$\begin{array}{l} x - 2 y + 3 z = 10 \\ 2 x + 5 y = 4 \\ y + 2 z = 2 \end{array}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

We are given the set of linear equations that is-

$\{\begin{cases} x - 2 y + 3 z = 10 \\ 2 x + 5 y = 4 \\ y + 2 z = 2 \end{cases}$

Step 2. Concept used

An equation that is presented by the combination of two variables and a constant is known as a linear equation.

Step 3. Calculation

The given system of equation is linear as all the equation in the system of equations has the form $a x + b y + c z + d = 0$ where $a, b, c, d$ are constants.

So, the given system of equations is linear.

Most popular questions for Math Textbooks

These exercises refer to the following system:

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

If we add $2$ times the first equation to the second equation, the second equation becomes_______ $=$ ________

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.

$\begin{array}{l} 4 x + 2 y = 16 \\ x - 5 y = 70 \end{array}$

Solving a General System of Equations Find x and y in

terms of a and b.

$\{\begin{cases} a x + b y = 0 \\ a^{2} x + b^{2} y = 1 \end{cases} (a \neq 0, b \neq 0, a \neq b)$

Find two numbers whose sum is 34 and

whose difference is 10.

Is the System of Equations Linear?

State whether the equation or system of equations is linear.

$x^{2} + y^{2} + z^{2} = 4$

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