system of linear inequalities
is a set of two or more linear inequalities containing two or more variables.
A system of linear inequalities refers to a set of two or more linear inequalities that are being solved simultaneously. Each inequality in the system represents a half-plane on a coordinate plane, and the intersection of these half-planes represents the solution set for the system of inequalities.
Here is an example of a system of linear inequalities:
x + y ≤ 5
2x – y > 3
To solve this system, we can graph each inequality on the same coordinate plane. The first inequality, x + y ≤ 5, represents the half-plane below the line x + y = 5. We can graph this line by plotting the intercepts (5,0) and (0,5) and connecting them with a straight line.
Similarly, the second inequality, 2x – y > 3, represents the half-plane above the line 2x – y = 3. We can graph this line by plotting the intercepts (0,-3) and (3/2,0) and connecting them with a straight line.
The solution set for this system of inequalities is the intersection of the two half-planes, which is the shaded region below the line x + y = 5 and above the line 2x – y = 3.
To write the solution set in interval notation, we can identify the region of the x-axis that is shaded and the region of the y-axis that is shaded. In this case, the shaded region includes all x values from 0 to 3/2, and all y values from 0 to 5.
Therefore, the solution set in interval notation is:
0 ≤ x ≤ 3/2, 0 ≤ y ≤ 5.
More Answers:
Understanding the Significance of Existence and Uniqueness in Solving Linear SystemsUnderstanding Matrix Dimensions: Debunking the Myth of Six Rows in a 5×6 Matrix
Discover the Vital Property of Elementary Row Operations in Linear Systems