
1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).
solution :
Let the cost of a notebook to be = ₹ x
Let the cost of a pen to be = ₹ y
According to the question,
Cost of a notebook = 2 × Cost of a pen
x=2×y
x=2y
x−2y=0
The cost of a notebook is twice the cost of a pen.
2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) 2x+3y=9.3ˉ5
(ii) x-y5-10=0
(iii) -2x+3y=6
(iv) x=3y
(v) 2x=-5y
(vi) 3x+2=0
(vii) y-2=0
(viii) 5=2x
solution :
(i) 2x+3y=9.3ˉ5
2x+3y=9.3ˉ5 can be written as 2x+3y-9.3ˉ5=0
Now, comparing 2x+3y-9.3ˉ5=0 with ax+by+c=0
Here,
a=2
b=3
c=-9.3ˉ5
(ii) x-y5-10=0
x-y5-10=0 can be written as 1x-15y-10=0
Now, comparing 1x-15y-10=0 with ax+by+c=0
Here,
a=1
b=15
c=-10
(iii) -2x+3y=6
-2x+3y=6 can be written as -2x+3y-6=0
Now, comparing -2x+3y-6=0 with ax+by+c=0
Here,
a=-2
b=3
c=-6
(iv) x=3y
x=3y can be written as 1x-3y+0=0
Now, comparing 1x-3y+0=0 with ax+by+c=0
Here,
a=1
b=-3
c=0
(v) 2x=-5y
2x=-5y can be written as 2x+5y+0=0
Now, comparing 2x+5y+0=0 with ax+by+c=0
Here,
a=2
b=5
c=0
(vi) 3x+2=0
3x+2=0 can be written as 3x+0y+2=0
Now, comparing 3x+0y+2=0 with ax+by+c=0
Here,
a=3
b=0
c=2
(vii) y-2=0
y-2=0 can be written as 0x+1y-2=0
Now, comparing 0x+1y-2=0 with ax+by+c=0
Here,
a=0
b=1
c=-2
(viii) 5=2x
5=2x can be written as -2x+0y+5=0
Now, comparing -2x+0y+5=0 with ax+by+c=0
Here,
a=-2
b=0
c=5
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