The document Ex 4.4 NCERT Solutions - Linear Equations in Two Variables Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Question 1. Give the geometric representations of y = 3 as an equation ****(i) in one variable ****(ii) in two variables****Solution: **(i) y = 3 [An equation in one variable]

âˆµ y = 3 is an equation in one variable, i.e. y only.

âˆ´ It has a unique solution y = 3 as shown on the number line shown here.

The unique solution is a point.

(ii) y = 3 [An equation in two variables]

We can write y = 3 as

0.x + y = 3

Now, when x = 1, y = 3

when x = 2, y = 3

when x = 3, y = 3

We get the following table:

x | 1 | 2 | 3 |

y | 3 | 3 | 3 |

Plotting the ordered pairs (1, 3), (2, 3) and (3, 3) on a graph paper, we get a line AB as solution of 0 . x + y = 3, i.e. y = 3.

**Question 2. Give the geometric representations of 2x + 9 = 0 as an equation (i) in one variable (ii) in two variables****Solution: **(i) 2x + 9 = 0 [An equation in one variable]

We have: 2x + 9 = 0

â‡’ 2x = â€“9

â‡’ x = (-9/2)

which is a linear equation in one variable â€˜xâ€™ only. Its solution is the point (-9/2) on the number line as shown below.

(ii) 2x + 9 = 0 [An equation in two variables]

We can write 2x + 9 = 0 as 2x + 0y + 9 = 0 or 2x = â€“9 + 0y

or

âˆ´ When y = 1,

When y = 2,

When y = 3,

Thus, we get the following table:

x | -9/2 | -9/2 | -9/2 |

y | 1 | 2 | 3 |

Now, plotting the ordered pairs on a graph paper and joining them, we get a line PQ as solution of 2x + 9 = 0.