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Q12.

Expert-verified

Algebra 2

Found in: Page 149

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

12: Solve each system of inequalities by graphing.
$\begin{matrix} 3 x + y < - 5 \\ 2 x - 4 y \geq 6 \end{matrix}$

The solution of the inequalities is $2 y + 3 \leq x < \frac{- 5 - y}{3}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step-1 – Concept of solution of linear inequalities

The solution of linear inequalities can be obtained by changing the inequalities into equations and solving the linear equations to obtain a graph. Then the common shaded region is a solution of the inequalities.

Step-2 – Concept of shading the region of the inequalities

The shaded region obtained by choosing a point, if the point satisfies the inequality the region is along the point, if not satisfies the inequalities, then the shaded region is opposite to the point.

Step-3 – Solving the inequalities

The given inequalities are-:

$\begin{matrix} 3 x + y < - 5 \\ 2 x - 4 y \geq 6 \end{matrix}$

The linear equation of the inequalities is-:

$\begin{matrix} 3 x + y = - 5 \\ 2 x - 4 y = 6 \end{matrix}$

The point which satisfies the equation $3 x + y = - 5$ are $(0, 5)$ and $(2, - 1)$ .

The point which satisfies the equation $2 x - 4 y = 6$ are $(3, 0)$ and $(1, - 1)$ .

Step-4 – Evaluating the shading region

We choose the point $(0, 0)$ . The point which $(0, 0)$ does not satisfy any of the inequalities $3 x + y < - 5$ and $2 x - 4 y \geq 6$ .

Step-5 – Plotting the graph

So, the graph of the inequality is

The common shaded region is $2 y + 3 \leq x < \frac{- 5 - y}{3}$ .

Most popular questions for Math Textbooks

Solve each system of equations by graphing.

$\begin{matrix} 3 x - 7 y = - 6 \\ x + 2 y = 11 \end{matrix}$

Solve the system of equations by graphing.

$\begin{matrix} 20 y + 13 x = 10 \\ 0.65 x + y = 0.5 \end{matrix}$

Solve each system of equations by graphing.

$\begin{matrix} \frac{2}{3} x + y = - 3 \\ y - \frac{1}{3} x = 6 \end{matrix}$

The sides of an angle are parts of two lines whose equations are $2 y + 3 x = - 7$ and $3 y - 2 x = 9$ . The angle’s vertex is the point where the two sides meet. Find the coordinates of the vertex of the angle.

Solve each system of equations by graphing.

$\begin{matrix} 23. \frac{1}{2} x - y = 0 \\ \frac{1}{4} x + \frac{1}{2} y = - 2 \end{matrix}$

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