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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