Problem 114

Question

Write a system of inequalities whose solution set includes every point in the rectangular coordinate system.

Step-by-Step Solution

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Answer

The system of inequalities that includes every point in the rectangular coordinate system is $x \geq 0$, $x \leq 0$, $y \geq 0$, $y \leq 0$.

1Step 1: Writing the inequalities for positive and negative values of 'x' and 'y'

First, considering the x-axis, since it includes all real numbers we write two inequalities: $x \geq 0$ and $x \leq 0$. Both of these inequalities put together cover all values on the x-axis. Similarly, considering the y-axis which also includes all real numbers, we write the inequalities: $y \geq 0$ and $y \leq 0$ representing all values on the y-axis.

2Step 2: Combine the inequalities

We put together all four inequalities to represent all points in the rectangular coordinate system. So, we find our system of inequalities to be: $x \geq 0$, $x \leq 0$, $y \geq 0$, $y \leq 0$. This system satisfies the requirement of the question.

Problem 109

Problem 115

Other exercises in this chapter

Problem 109

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Problem 109

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Problem 115

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Problem 116

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