There are infinite points in the solution set of system of inequalities and .
Further explanation:
Given:
The system of inequalities is given as follows:
Calculation:
The set of inequalities are,
…… (1)
…… (2)
Both the inequalities are strict inequalities; therefore they are graphed with dashed lines.
The corresponding equation of inequality (1) can be expressed as follows:
…… (3)
The corresponding equation of inequality (2) can be expressed as follows:
…… (4)
Multiply equation (3) by as shown below:
Subtract equation (5) from equation (4) as follows:
Simplify equation to find the value of as follows:
Substitute for in equation (4) to obtain the value of as follows:
Add on both sides of above equation as follows:
Now, divide both sides by 2 as follows:
The intersection of the lines and is the point .
Consider test point as .
Substitute for and for in inequality (1) as follows:
The point satisfies the inequality (1) and this point lies above the line .
Substitute for and for in inequality (2) as follows:
The point satisfies the inequality (2) and this point lies below the line .
The graph of the solution set is the shaded region as shown in Figure 1 (attached in the end).
The solution set is the common region for both the regions of inequalities and .
There can be infinite number of points in the solution set of both the inequalities.
Therefore, there are infinite points in the solution set of system of the given inequalities.
Learn more:
1. Learn more about equations brainly.com/question/1473992
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear Inequalities
Keywords: Point, solution set, system, inequalities, 3x+y>-3, x+2y<4, (-2, 3), graph, linear, strict, infinite, intersection, dashed, infinte points, common region, shded region, inequalities, equation.