Which Quadrant Contains No Solutions to This System of Inequalities?

In summary, an inequality graph is a visual representation of a mathematical inequality, using symbols such as <, >, ≤, or ≥ to compare two quantities. To graph an inequality, we plot the boundary line and shade the region above or below it depending on the inequality symbol. Inequality graphs show a range of values, while equality graphs show a specific value. In real life, inequality graphs are used in economics and social sciences to analyze income distribution and make decisions about resource allocation. The key features of an inequality graph include the boundary line, shading, and inequality symbol, as well as the x and y axes and the origin.
  • #1
kamranpiriyev
1
0
If the system of inequalities y ≥ 2x + 1 and y> x/2-1
is graphed in the xy-plane above, which
quadrant contains no solutions to the system?
A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants.


I thing the answer is D . But book says that it is C. I think C is wrong 'cause from the second inequality we can get (1;-1/2) or (2;-1) which are in 4 quadrant
 
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  • #2
?? No, they are not! [tex]-\frac{1}{2}[/tex] is NOT larger than [tex]2\left(-\frac{1}{2}\right)+ 1= 0. And [tex]-1[/tex] is NOT larger than [tex]2\left(2\right)+ 1= 5[/tex].

Is it possible that you are thinking "(y, x)" rather than "(x, y)"?
 
  • #3
kamranpiriyev said:
If the system of inequalities y ≥ 2x + 1 and y> x/2-1
is graphed in the xy-plane above, which
quadrant contains no solutions to the system?
A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants.


I thing the answer is D . But book says that it is C. I think C is wrong 'cause from the second inequality we can get (1;-1/2) or (2;-1) which are in 4 quadrant

Let's graph the system of inequalities:

[desmos="-10,10,-10,10"]y\ge2x+1;y\gt x/2-1[/desmos]

From this we can see quadrants I-III contain solutions, and quadrant IV has no solutions. :)
 

Related to Which Quadrant Contains No Solutions to This System of Inequalities?

1. What is an inequality graph?

An inequality graph is a visual representation of a mathematical inequality, which is a statement that compares two quantities using inequality symbols such as <, >, ≤, or ≥. The graph shows all possible solutions to the inequality and can help us understand the relationship between the two quantities.

2. How do you graph an inequality?

To graph an inequality, we first plot the boundary line using an equal sign, then shade the region above or below the line depending on the inequality symbol. If the boundary line is included in the solution, we use a solid line; if it is not included, we use a dashed line. We also label the shaded region with an inequality symbol to indicate which values are included in the solution.

3. What is the difference between an inequality graph and an equality graph?

An inequality graph shows a range of values that satisfy a mathematical inequality, while an equality graph shows a specific value that satisfies a mathematical equation. Inequality graphs use shading to represent a range of values, while equality graphs use a single point or line to represent a specific value.

4. How can an inequality graph be used in real life?

Inequality graphs are commonly used in economics and social sciences to analyze and represent income distribution, wealth disparities, and other forms of inequality. They can also be used to make decisions about resource allocation, such as determining the minimum and maximum production levels for a factory.

5. What are the key features of an inequality graph?

The key features of an inequality graph include the boundary line, shading, and inequality symbol. The boundary line represents the equality part of the inequality, while the shading and inequality symbol indicate the direction and extent of the inequality. Additionally, the x and y axes represent the two quantities being compared, and the origin (0,0) is often used as a reference point.

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