Q1. 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)
Ans: Let the cost of a notebook be = ₹ x
Let the cost of a pen be = ₹ y
According to the question,
The cost of a notebook is twice the cost of a pen.
i.e., cost of a notebook = 2×cost of a pen
x = 2 × y
x = 2y
x  2y = 0
x  2y = 0 is the linear equation in two variables to represent the statement, ‘The cost of a notebook is twice the cost of a pen.’
Q2. 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=
Ans: Consider 2x + 3y= Equation (1)
⇒ 2x + 3y  = 0
Comparing this equation with the standard form of the linear equation in two variables, ax + by + c = 0 we have,
a = 2
b = 3
c = 
(ii) x – (y/5) – 10 = 0
Ans: The equation x –(y/5)10 = 0 can be written as,
(1)x+(1/5)y +(–10) = 0
Now comparing x+(1/5)y+(–10) = 0 with ax+by+c = 0
We get,
a = 1
b = (1/5)
c = 10
(iii) –2x + 3y = 6
Ans: –2x+3y = 6
Rearranging the equation, we get,
–2x+3y–6 = 0
The equation –2x+3y–6 = 0 can be written as,
(–2)x+(3)y+(– 6) = 0
Now, comparing (–2)x+(3)y+(–6) = 0 with ax+by+c = 0
We get, a = –2
b = 3
c =6
(iv) x = 3y
Ans: x = 3y
Rearranging the equation, we get,
x3y = 0
The equation x3y=0 can be written as,
(1)x+(3)y+(0)c = 0
Now comparing 1x+(3)y+(0)c = 0 with ax+by+c = 0
We get a = 1
b = 3
c = 0
(v) 2x = –5y
Ans: 2x = –5y
Rearranging the equation, we get,
2x+5y = 0
The equation 2x+5y = 0 can be written as,
2x+5y+0 = 0
Now, comparing (2)x+(5)y+0= 0 with ax+by+c = 0
We get a = 2
b = 5
c = 0
(vi) 3x + 2 = 0
Ans: 3x+2 = 0
The equation 3x+2 = 0 can be written as,
3x+0y+2 = 0
Now comparing 3x+0+2= 0 with ax+by+c = 0
We get a = 3
b = 0
c = 2
(vii) y–2 = 0
Ans: y–2 = 0
The equation y–2 = 0 can be written as,
(0)x+(1)y+(–2) = 0
Now comparing (0)x+(1)y+(–2) = 0with ax+by+c = 0
We get a = 0
b = 1
c = –2
(viii) 5 = 2x
Ans: 5 = 2x
Rearranging the equation, we get,
2x = 5
i.e., 2x–5 = 0
The equation 2x–5 = 0 can be written as,
2x+0y–5 = 0
Now comparing 2x+0y–5 = 0 with ax+by+c = 0
We get a = 2
b = 0
c = 5
1. What are linear equations in two variables? 
2. How do you solve a system of linear equations in two variables? 
3. What is the importance of linear equations in two variables? 
4. Can linear equations in two variables have more than one solution? 
5. What is the graphical representation of linear equations in two variables? 
62 videos426 docs102 tests

62 videos426 docs102 tests
