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Introduction - Pair of Linear Equations in Two Variables Video Lecture - Class 10
FAQs on Introduction - Pair of Linear Equations in Two Variables Video Lecture - Class 10
| 1. What are linear equations in two variables? |  |
Ans. Linear equations in two variables are algebraic equations that involve two variables, usually represented as x and y, with a constant coefficient for each variable and a constant term. They can be written in the form ax + by = c, where a, b, and c are real numbers.
| 2. How many solutions can a pair of linear equations in two variables have? | |
Ans. A pair of linear equations in two variables can have three types of solutions:
1) Unique solution: If the lines representing the equations intersect at a single point, then the pair of equations has a unique solution.
2) Infinitely many solutions: If the lines representing the equations coincide or are identical, then the pair of equations has infinitely many solutions.
3) No solution: If the lines representing the equations are parallel and never intersect, then the pair of equations has no solution.
| 3. How can we solve a pair of linear equations in two variables graphically? | |
Ans. To solve a pair of linear equations in two variables graphically, we plot the lines representing the equations on a coordinate plane. The solution to the system of equations is the point of intersection of the two lines. If the lines do not intersect or are parallel, then the system has no solution or infinitely many solutions, respectively.
| 4. What is the substitution method for solving a pair of linear equations in two variables? | |
Ans. The substitution method is a technique used to solve a pair of linear equations in two variables algebraically. In this method, we solve one equation for one variable and substitute the expression obtained into the other equation. This allows us to solve for the remaining variable. The obtained values can then be substituted back into either of the original equations to find the values of both variables.
| 5. Can linear equations in two variables be solved using matrices? | |
Ans. Yes, linear equations in two variables can be solved using matrices. This method is known as the matrix method or the method of elimination. The coefficients of the variables and the constant terms are organized into matrices, and a series of row operations are performed to transform the system of equations into an equivalent system with simpler equations. The resulting matrix can then be used to find the values of the variables.
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