lass IX Math NCERT Solution for Linear Equations in Two Variables 4.4

EXERCISE: 4.4
1.   Give the geometric representations of y = 3 as an equation
      (i) in one variable      (ii) in two variables
Sol: (i) y = 3 [An equation in one variable]
           ∵ y = 3 is an equation in one variable, i.e. y only.
           ∴ 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:
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.
2.   Give the geometric representations of 2x + 9 = 0 as an equation
      (i) in one variable      (ii) in two variables
Sol: (i) 2x + 9 = 0 [An equation in one variable]
           We have: 2x + 9 = 0 ⇒ 2x = –9
           
      Which is a linear equation in one variable 'x' only. Its solution is the point 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 = –9 + 0y
           
      Thus, we get the following table:
      Now, plotting the ordered pairs  on a graph paper and joinging them, we get a line PQ as solution of 2x + 9 = 0.

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