Chapter 4: Q. 297 (page 472)

In the following exercises, solve each system by graphing $\{\begin{cases} 2 x + y > - 6 \\ - x + 2 y \geq - 4 \end{cases}$

Short Answer

Expert verified

The darkest region represent the solution to the system of equations

Step by step solution

Given information

Given the system of equations $\{\begin{cases} 2 x + y > - 6 \\ - x + 2 y \geq - 4 \end{cases}$

Checking the point

The equation $2 x + y = 6$ has intercept $6, 3$ . Testing the point $(0, 0)$ , we get

$2 (0) + 0 > - 6 0 + 0 > - 6 0 > - 6$ which is true

So origin is included

Checking for another equation

The equation $- x + 2 y = - 4$ has intercept $- 2, 4$ .Testing the point $(0, 0)$ , we get

$- 0 + 2 (0) \geq - 4 0 + 0 \geq - 4 0 \geq - 4$ which is true

So origin is included

Sketching the graph

The graph is

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In the following exercises, solve each system by graphing $\{\begin{cases} 2 x + y > - 6 \\ - x + 2 y \geq - 4 \end{cases}$

Short Answer

Step by step solution

Given information

Checking the point

Checking for another equation

Sketching the graph

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In the following exercises, solve each system by graphing 2x+y>-6-x+2y≥-4

Short Answer

Step by step solution

Given information

Checking the point

Checking for another equation

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Pure Maths

Geometry

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing $\{\begin{cases} 2 x + y > - 6 \\ - x + 2 y \geq - 4 \end{cases}$