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CBSE Class 9 Mathematics Question 8 of 9

Linear Equations in Two Variables — Question 4

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4
Question

Question 2(iii)

Write four solutions for the following equations:

x = 4y

Answer

Given, equation :

⇒ x = 4y

Substituting x = 0, in the given equation, we get :

⇒ 0 = 4y

⇒ y = 04\dfrac{0}{4}

⇒ y = 0

∴ Solution is (0, 0).

Substituting x = 1, in the given equation, we get :

⇒ 1 = 4y

⇒ y = 14\dfrac{1}{4}.

∴ Solution is (1,14)\Big(1, \dfrac{1}{4}\Big).

Substituting x = 4, in the given equation, we get :

⇒ 4 = 4y

⇒ y = 44\dfrac{4}{4}

⇒ y = 1

∴ Solution is (4, 1).

Substituting x = -4, in the given equation, we get :

⇒ -4 = 4y

⇒ y = −44\dfrac{-4}{4}

⇒ y = -1

∴ Solution is (-4, -1).

Hence, solutions for equation x = 4y are (0, 0), (1,14)(1, \dfrac{1}{4}\Big), (4, 1) and (-4, -1).

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Mathematics | Linear Equations in Two VariablesWeb Content • Interactive Notes

Linear Equations in Two Variables — Interactive Study Guide

Infinite Solutions

A linear equation in two variables has infinitely many solutions. Each solution is a point on the line. The line extends forever in both directions.

Key Concept: One equation, two unknowns = infinite solutions. You need TWO equations to get a unique solution (Class X topic).

Graphing Made Easy

  1. Rewrite as y = mx + c.
  2. Make a table: choose 3 values of x, calculate y for each.
  3. Plot the 3 points. If they’re collinear, draw the line.

Special Lines

y = 3: Horizontal line, 3 units above x-axis.

x = −2: Vertical line, 2 units left of y-axis.

y = x: Line at 45° through origin.

Quick Self-Check

  1. Is (2, 3) a solution of x + y = 5? (Yes: 2 + 3 = 5)
  2. Give 3 solutions of y = 2x. ((0,0), (1,2), (2,4))
  3. What is the equation of the x-axis? (y = 0)

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