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Q. 1

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 795

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} - 2 x + y = - 7 \\ 4 x + 3 y = 9 \end{cases}$

The solution of the system of equations $\{\begin{cases} - 2 x + y = - 7 \\ 4 x + 3 y = 9 \end{cases}$ is $(3, - 1)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The system of equations:

$\{\begin{cases} - 2 x + y = - 7 \\ 4 x + 3 y = 9 \end{cases}$

Step 2. Solve the equation

Multiply the first equation by $2$ ,

$- 4 x + 2 y = - 14$

Add the above equation with second equation, we get,

$5 y = - 5 y = - 1$

Step 3. Find x

Substitute $y = - 1$ in the second equation,

$4 x + 3 y = 9 4 x + 3 (- 1) = 9 4 x = 12 x = 3$

Step 4. Check the solution

Substitute $x = 3; y = - 1$ in the first equation,

$- 2 x + y = - 7 - 2 (3) + (- 1) = - 7 - 7 = - 7$

Hence the solution is checked.

Most popular questions for Math Textbooks

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{cases} 2 x + y \geq - 2 \\ 2 x + y \geq 2 \end{cases}$

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{array}{r} \begin{array}{rcl} 4 x - z & = & 7 \\ 8 x + 5 y - z & = & 0 \end{array} \\ - x - y + 5 z = 6 \end{array} x = 2, y = - 3, z = 1; (2, - 3, 1)$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}$

solve each system of equations. If the system has no solution, say that it is inconsistent.

$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

The altitude of an isosceles triangle drawn to its base is $3 c m$ , and its perimeter is $18 c m$ . Find the length of its base.

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