Chapter 3: Q46. (page 135)

Solve each system of inequalities by graphing.
46. $\begin{matrix} 2 y + x \geq 4 \\ y \geq x - 4 \end{matrix}$ .

Short Answer

Expert verified

The solution set of the given system of inequalities is shown in the below graph:

Step by step solution

– Sketch the solution of the inequality 2y+x≥4.

Solve the equation $2 y + x \geq 4$ for y:

$\begin{matrix} 2 y + x \geq 4 \\ 2 y \geq - x + 4 \\ y \geq - \frac{x}{2} + \frac{4}{2} \\ y \geq - \frac{x}{2} + 2 \end{matrix}$

The equation of the inequality $y \geq - \frac{x}{2} + 2$ is $y = - \frac{x}{2} + 2$ which is a line equation with slope $m = - \frac{1}{2},$ and the $y -$ intercept is $(0, 2)$ .

Graphical interpretation of the given inequality $2 y + x \geq 4$ :

– Sketch the solution of the inequality y≥x-4 .

The equation of the inequality $y \geq x - 4$ is $y = x - 4$ which is a line equation with slope $m = 1$ and the $y -$ intercept is $(0, - 4)$ .

Graphical interpretation of the given inequality $y \geq x - 4$ :

– Now sketch the solution set of the both the inequalities in the coordinate plane.

The solution set is the region colored in purple.

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Solve each system of inequalities by graphing.
46. $\begin{matrix} 2 y + x \geq 4 \\ y \geq x - 4 \end{matrix}$ .

Short Answer

Step by step solution

– Sketch the solution of the inequality 2y+x≥4.

– Sketch the solution of the inequality y≥x-4 .

– Now sketch the solution set of the both the inequalities in the coordinate plane.

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Solve each system of inequalities by graphing.46. 2y+x≥4y≥x−4.

Short Answer

Step by step solution

– Sketch the solution of the inequality 2y+x≥4.

– Sketch the solution of the inequality y≥x-4 .

– Now sketch the solution set of the both the inequalities in the coordinate plane.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each system of inequalities by graphing.
46. $\begin{matrix} 2 y + x \geq 4 \\ y \geq x - 4 \end{matrix}$ .