Chapter 4: Q 290 (page 472)

In the following exercises, solve each system by graphing.
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$

Short Answer

Expert verified

The darkest region represent the solution to the system of equations and the graph is

Step by step solution

Given information

Given the system of equations $\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$

Checking the point for the system of equations

The equation $x - y = 1$ has intercept $- 1, 1$ . Testing the point $(0, 0)$ , we get

$0 - 0 > 1 0 > 1$

So origin is not included

Checking for the another system of equation

The equation $y = - \frac{1}{4} x + 3$ has intercept $3, 12$ . Testing the point $(0, 0)$ , we get

$0 < 0 + 3 0 < 3$ which is true

So origin is included

Graphing the equation

The graph of the equations is

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In the following exercises, solve each system by graphing.
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$

Short Answer

Step by step solution

Given information

Checking the point for the system of equations

Checking for the another system of equation

Graphing the equation

One App. One Place for Learning.

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In the following exercises, solve each system by graphing. x-y>1y<-14x+3x-y>1y<-14x+3

Short Answer

Step by step solution

Given information

Checking the point for the system of equations

Checking for the another system of equation

Graphing the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Calculus

Pure Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing.
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$
$\{\begin{cases} x - y > 1 \\ y < - \frac{1}{4} x + 3 \end{cases}$