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Graphical Solution of Linear Inequalities in 2 variables Video Lecture | Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

FAQs on Graphical Solution of Linear Inequalities in 2 variables Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is a linear inequality in 2 variables?
Ans. A linear inequality in 2 variables is an inequality that can be expressed in the form ax + by < c or ax + by > c, where a, b, and c are constants, and x and y are the variables. It represents a region on a coordinate plane that satisfies the inequality.
2. How do you graph a linear inequality in 2 variables?
Ans. To graph a linear inequality in 2 variables, follow these steps: 1. Rewrite the inequality in slope-intercept form (y = mx + b), if necessary. 2. Plot the y-intercept (b) on the y-axis. 3. Use the slope (m) to find additional points on the line. 4. Draw a dashed or solid line through the points, depending on whether the inequality is strict or non-strict. 5. Test a point not on the line to determine which side of the line satisfies the inequality. 6. Shade the region above or below the line accordingly.
3. How do you determine the solution to a system of linear inequalities graphically?
Ans. To determine the solution to a system of linear inequalities graphically, follow these steps: 1. Graph each inequality separately on the same coordinate plane. 2. Identify the region of overlap where the shaded regions of the inequalities intersect. 3. The solution to the system of inequalities is the set of points within the shaded region of overlap.
4. Can a system of linear inequalities have no solution?
Ans. Yes, a system of linear inequalities can have no solution. This occurs when the shaded regions of the individual inequalities do not overlap, resulting in an empty region where no points satisfy all the inequalities simultaneously.
5. How can you use the graphical solution of linear inequalities in 2 variables in real-life scenarios?
Ans. The graphical solution of linear inequalities in 2 variables can be used in various real-life scenarios, such as: - Optimizing production or resource allocation in a business by identifying feasible regions. - Determining the range of values for variables in financial planning or budgeting. - Analyzing inequalities in social sciences, such as studying economic disparities or educational opportunities. - Solving problems related to geometry or physics, where constraints are represented by inequalities. - Analyzing supply and demand relationships in economics to find equilibrium points.
209 videos|443 docs|143 tests

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