Introduction to Linear Equation in Two Variables MCQs Quiz | Class 9

This quiz covers Unit II: Algebra for Class IX Mathematics (Code 041), focusing on the introduction to linear equations in two variables. Key topics include the meaning of two variables and the standard form ax + by + c = 0. Test your understanding, check your score, and click “Download Answer PDF” to save your results for revision.

Unit II: Algebra – Linear Equations in Two Variables Overview

In Class IX Mathematics (Code 041), Unit II introduces the concept of linear equations involving two distinct variables. Understanding this foundation is crucial for coordinate geometry and algebraic graphing.

1. Standard Form

Any equation that can be put in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. The variables are usually denoted by x and y.

  • a is the coefficient of x.
  • b is the coefficient of y.
  • c is the constant term.

2. Important Characteristics

Feature Description
Degree The highest power of variables is 1. If the power is 2 or more, it is not linear.
Solutions A linear equation in two variables has infinitely many solutions. Every point on its graph represents a solution.
Graph The graph of a linear equation in two variables is always a straight line.

3. Special Cases

Often equations appear with only one variable but can be expressed as two variables:

  • Equation x = a: Can be written as 1.x + 0.y = a. Its graph is a line parallel to the Y-axis.
  • Equation y = b: Can be written as 0.x + 1.y = b. Its graph is a line parallel to the X-axis.
  • Equation y = mx: Represents a line passing through the origin (0,0).

Quick Revision Points

  1. The equation x = 0 represents the Y-axis.
  2. The equation y = 0 represents the X-axis.
  3. Values of x and y that satisfy the equation ax + by + c = 0 are called the solution of the equation.
  4. To find solutions, you can assume a value for x and calculate the corresponding value of y (or vice versa).

Extra Practice Questions

Try solving these without the quiz interface:

  1. Express 2x = 5 in the form ax + by + c = 0.
  2. Find two solutions for the equation 4x + 3y = 12.
  3. Determine if (1, 1) is a solution to 2x – 3y = 5.
  4. Write the equation of a line parallel to the x-axis at a distance of 3 units above it.
  5. If x = 2k – 1 and y = k is a solution of 3x – 5y = 7, find the value of k.