Chapter 4: Q 293 (page 472)

In the following exercises, solve each system by graphing $\{\begin{cases} 2 x + 4 y \geq 8 \\ y \leq \frac{3}{4} x \end{cases}$

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 $\{\begin{cases} 2 x + 4 y \geq 8 \\ y \leq \frac{3}{4} x \end{cases}$

Checking the point

The equation, $2 x + 4 y = 8$ has the intercept $2, 4$ . Testing the point $(0, 0)$ , we get

$2 (0) + 4 (0) \geq 8 0 + 0 \geq 8 0 \geq 8$ which is not true

So origin is not included

Checking for another point

The equation, $y = \frac{3}{4} x$ Testing the point $(0, 0)$ , we get

$0 \leq \frac{3}{4} (0) 0 \leq 0$ 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 $\{\begin{cases} 2 x + 4 y \geq 8 \\ y \leq \frac{3}{4} x \end{cases}$

Short Answer

Step by step solution

Given information

Checking the point

Checking for another point

Sketching the graph

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In the following exercises, solve each system by graphing 2x+4y≥8y≤34x

Short Answer

Step by step solution

Given information

Checking the point

Checking for another point

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve each system by graphing $\{\begin{cases} 2 x + 4 y \geq 8 \\ y \leq \frac{3}{4} x \end{cases}$