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Chapter 7: Problem 65

Without graphing, Determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}6 x-y \leq 24 \\ 6 x-y>24\end{array}\right.\)

Short Answer

Expert verified
The system has no solution.

Step by step solution

01

Understand the given inequalities

The given system of inequalities are 6x - y 鈮� 24 and 6x - y > 24. Both inequalities have the same coefficients for x and y, which means they represent the same line. However, one accepts values that are less than or equal to 24, while the other only accepts values that are strictly greater than 24.
02

Compare the two inequalities

As we can see, for a point to satisfy both inequalities, it has to be both less than or equal to 24 and greater than 24. This is impossible, as a number cannot be less than or equal to 24 and also strictly more than 24. Therefore, there is no solution as no point in the plane could satisfy both inequalities simultaneously.

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Most popular questions from this chapter

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(f(x)=x^{2}-2 x-8\)

Graph each linear inequality. \(2 x+3 y>12\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x+2 y \leq 4 \\ y \geq x-3\end{array}\right.\)

Graph each linear inequality. \(y \leq 3 x+2\)

In Exercises 23-38, graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}3 x+6 y \leq 6 \\ 2 x+y \leq 8\end{array}\right.\)
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