# Linear Equations in Two Variables : Exercise 4.4 (Mathematics NCERT Class 9th)

**Q.1Â Â Â Â Â Give the geometric representation of y = 3 as an equation.**

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i) in one variable Â Â Â Â Â Â Â (ii) in two variables**

**Sol.**

(i) The representation of the solution on theÂ number when y = 3 is treated as an equation in one variable is as under

(ii)Â We know that y = 3 can be written as 0. x + y = 3 as a linear equation in variables x and y. Now all the values of x are permissible as 0. x is always 0. However, y must satisfy theÂ relation y = 3.

Hence , threeÂ solution of the given equation are

x = 0, y = 3 ; Â Â Â x = 2, y = 3 Â ; Â Â x = - 2 , y = 3

Plotting theÂ points (0, 3) (2, 3) andÂ (â€“2, 3) and on joining them we get the graph AB as a lineÂ parallel to x-axis at a distance of 3 units above it.

**Q.2Â Â Â Â Â Â Given the geometric representations of 2x + 9 = 0Â as an equation.**

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i)Â in oneÂ variable Â Â Â Â Â Â Â Â Â (ii)Â in two variables**

**Sol. **

(i) TheÂ representation of the solution on the number line 2x + 9 = 0 i.e., is treated as anÂ equation in one variable is as under.Â (ii) We knowÂ that 2x + 9 = 0 can be written as 2x + 0y + 9Â = 0 as a linear equation in variables x and y. Now all theÂ values of x areÂ permissibleÂ as 0. y is always 0. However, x mustÂ satisfy the relation 2x + 9 = 0

i.e., .

Hence three solution of theÂ givenÂ equation areÂ ,y = 0 ; ,y = 2 and ,y =â€“ 2.

ThereforeÂ PlottingÂ the point and onÂ joining them we get the graph AB as a lineÂ parallel to y-axis at a distance of on the left of y-axis.

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