Exercise 6.1

1.Express the following linear equation in the form of ax+by+c=0 and indicate the values of a, b and c in each case.

i) 8x + 5y − 3 = 0

sol.8x+5y-3=0

$$\Rightarrow$$ 8x+5y+(-3)=0      Here a=8,b=5 and c=-3

ii)28x-35y=-7

sol.28x-35y=-7

$$\Rightarrow$$ 28x+(-35)y+7=0 Here a=28,b=-35 and c=7

iii)93x=12-15y

sol.93x=12-15y

$$\Rightarrow$$ 93x+15y-12=0 $$\Rightarrow$$ 93x+15y+(-12)=0   Here a=93, b=15 and c=-12

iv)2x=-5y

sol.2x=-5y

$$\Rightarrow$$ 2x+5y=0     Here a=2,b=5 andc=0

v)

$$\frac{x}{3}+\frac{y}{4}$$ =7

sol.

$$\frac{x}{3}+\frac{y}{4}$$ =7 $$\Rightarrow \frac{x}{3}+\frac{y}{4}-7$$ =0 $$\Rightarrow \frac{4x+3y-84}{12}$$ =0 $$\Rightarrow$$ 4x+3y-84=0

Here a=4,b=3 and c=-84

vi)y=

$$-\frac{3}{2}x$$

sol.y=

$$-\frac{3}{2}$$ x $$\Rightarrow$$ 2y=-3x $$\Rightarrow$$ 3x+2y=0     Here a=3,b=2 and c=0

vii)3x+5y=12

sol.3x+5y=12

$$\Rightarrow$$ 3x+5y+(-12)=0             Here a=3,b=5 and c=-12

2.Write each of the following in the form of ax+by+c=0 and find the values of a,b and c.

i)2x=5               

sol.2x-5=0

a=2

b=0

c-=-5

ii)y-2=0

sol.y-2=0

a=0

b=1

c=-2

iii)

$$\frac{y}{7}$$ =3

sol.

$$\frac{y}{7}$$ =3

y=21

y-21=0

a=0

b=1

c=-21

iv)x=

$$\frac{-14}{13}$$

sol.x=

$$\frac{-14}{13}$$

$$\Rightarrow$$ 13x=-14

$$\Rightarrow$$ 13x+14=0

a=13

b=0

c=14

3.Express the following statements as a linear equation in two variables.

i)The sum of two numbers is 34.

Sol.x+y=34; x,y are any two numbers

$$\Rightarrow$$ x+y-34=0

ii)The cost of a ball pen is Rs/-5 less than half the cost of a fountain pen.

Sol.Let the cost of a fountain pen =x

Let the cost of ball pen =y

Then y=x-5 or x-y-5=0

iii)Bhargavi got 10more marks than double of the marks of sindhu.

Sol.Let sindhu’s marks =x

Bhargavi’s marks =y

Then by problem y=2x+10 or 2x-y+10=10

iv)The cost of a pencil is ` 2 and a ball point pen is 15. Sheela pays Rs/-100 for the pencils and pens she purchased.

Sol.Given that cost of a pencil=Rs/-2

Cost of a ball point pen =Rs/-15

Let the number of pencils purchased =x

Let the number of pens purchased =y

Then the total cost of x-pencils =2x

Then the total cost of y-pens =15y

By problem 2x+15y=100

v)Yamini and Fatima of class IX together contributed 200/- towards the Prime Minister’s Relief Fund.

Sol.Let yamini’s contribution to PMRF be =Rs/-x

Fatima’s contribution to PMRF be =Rs/-y

Then by problem x+y=200

vi)The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If the digits in units and ten’s place are x and y respectively.

Sol.Let the number be 10y+x

Number obtained by reversing its digits 10x+y

$$\therefore$$ sum of the numbers =(10y+x)+(10x+y)=11x+11y

by problem 11x+11y=121

$$\Rightarrow$$ x+y= $$\frac{121}{11}\Rightarrow$$ x+y=11

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