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Example - Pair of Linear Equation in Two Variable Video Lecture - Class 10

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FAQs on Example - Pair of Linear Equation in Two Variable Video Lecture - Class 10

1. What is a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables and have a degree of one. These equations can be represented graphically as two straight lines and can be solved simultaneously to find the values of the variables that satisfy both equations.
2. How can we solve a pair of linear equations in two variables?
Ans. There are multiple methods to solve a pair of linear equations in two variables. One commonly used method is the substitution method, where we solve one equation for one variable and substitute it into the other equation. Another method is the elimination method, where we manipulate the equations to eliminate one variable and solve for the other. Graphical method and matrix method are also used to solve linear equations in two variables.
3. Can a pair of linear equations in two variables have more than one solution?
Ans. Yes, a pair of linear equations in two variables can have three types of solutions: 1. Unique Solution: When the two lines representing the equations intersect at a single point, the system has a unique solution. This means that there is only one set of values for the variables that satisfy both equations. 2. No Solution: If the two lines representing the equations are parallel and do not intersect at any point, the system has no solution. This means that there are no values for the variables that satisfy both equations simultaneously. 3. Infinite Solutions: When the two lines representing the equations coincide or overlap, the system has infinitely many solutions. This means that any point on the line represents a solution, and there are infinitely many values for the variables that satisfy both equations.
4. How can we graphically represent a pair of linear equations in two variables?
Ans. To graphically represent a pair of linear equations in two variables, we plot the points that satisfy each equation on a coordinate plane. The two lines are then drawn connecting these points. The point of intersection (if it exists) represents the solution to the system of equations. If the lines are parallel, there is no solution, and if the lines coincide, there are infinitely many solutions.
5. What is the significance of solving a pair of linear equations in two variables?
Ans. Solving a pair of linear equations in two variables has various applications in real-life scenarios. It helps in finding the values of unknown quantities, determining the break-even point in business, analyzing supply and demand, optimizing resources, and solving problems related to distance, speed, and time. The ability to solve these equations enables us to make informed decisions and solve complex problems in different fields such as economics, engineering, and physics.
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