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NCERT Textbook: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10
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FAQs on NCERT Textbook: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10
| 1. What is a pair of linear equations in two variables? |  |
Ans. A pair of linear equations in two variables is a system of two equations with two variables, typically represented as x and y. These equations can be solved simultaneously to find the values of x and y that satisfy both equations.
| 2. How can we solve a pair of linear equations in two variables? | |
Ans. There are various methods to solve a pair of linear equations in two variables. One common method is the substitution method, where one equation is solved for one variable and then substituted into the other equation. Another method is the elimination method, where both equations are manipulated to eliminate one variable, allowing the other variable to be solved for.
| 3. Can a pair of linear equations in two variables have no solution? | |
Ans. Yes, a pair of linear equations in two variables can have no solution. This occurs when the lines represented by the equations are parallel and do not intersect. Geometrically, this means that the system of equations represents two lines that are not coincident and do not intersect at any point.
| 4. Can a pair of linear equations in two variables have infinitely many solutions? | |
Ans. Yes, a pair of linear equations in two variables can have infinitely many solutions. This occurs when the lines represented by the equations are coincident, meaning they are the same line. Geometrically, this means that the system of equations represents two lines that overlap completely, intersecting at every point along the line.
| 5. 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 can plot the equations on a coordinate plane. Each equation represents a line, and the point of intersection between the two lines represents the solution to the system of equations. By plotting points on the graph and connecting them, we can visualize the relationship between the two equations and find their solution.
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