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Index: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10

(a) Introduction

(b) Solutions of a Linear Equations

(c) Graph of a Linear Equation in Two Variables

(d) Equations of Lines Parallel to the x-axis & y-axis

(e) General

(f) R.D. Sharma & R.S. Aggarwal

(g) NCERT Textbook & Exercise Solutions

(h) Worksheet Questions

(i) Previous Year Questions

(j) Test Your Knowledge

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FAQs on Index: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10

1. What are the methods to solve a pair of linear equations in two variables?
Ans. The three main methods to solve a pair of linear equations in two variables are: 1. Graphical Method: Plotting both equations on a graph to find the point of intersection. 2. Substitution Method: Solving one equation for one variable and substituting that expression into the other equation. 3. Elimination Method: Adding or subtracting the two equations to eliminate one variable, making it easier to solve for the other.
2. What is the general form of a linear equation in two variables?
Ans. The general form of a linear equation in two variables is expressed as Ax + By + C = 0, where A, B, and C are constants, and A and B are not both zero. Here, x and y are the variables.
3. How can we determine if a pair of linear equations is consistent or inconsistent?
Ans. A pair of linear equations is considered consistent if they have at least one solution, which occurs when the lines intersect at a point or are the same line (infinitely many solutions). Conversely, they are inconsistent if they represent parallel lines and do not intersect, indicating that there is no solution.
4. What does it mean if two linear equations are dependent?
Ans. Two linear equations are said to be dependent if they represent the same line, meaning they have infinitely many solutions. In this case, one equation can be expressed as a multiple of the other, indicating that they are not distinct but essentially the same.
5. How do you graphically represent a pair of linear equations?
Ans. To graphically represent a pair of linear equations, you first convert each equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Then, plot the y-intercept on the graph and use the slope to find another point. Repeat this for the second equation, and where the two lines intersect represents the solution to the equations.
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