Class 9 - Mathematics
Linear Equations in Two Variables - Exercise 4.1
Top Block 1
Exercise 4.1
Question : 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 Rs x and that of a pen to be Rs y).
Answer :
Let the cost of a notebook = Rs x
The cost of a pen = y
According to the condition, we have
Cost of a notebook = 2 * Cost of a pen
⇒ x = 2 * y
⇒ x = 2y
⇒ x – 2y = 0
This is the required linear equation.
Question : 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 = 9.35 (ii) x – y/5 – 10 = 0 (iii) –2x + 3y = 6 (iv) x = 3y
(v) 2x = –5y (vi) 3x + 2 = 0 (vii) y – 2 = 0 (viii) 5 = 2x
Answer :
(i) 2x + 3y = 9.35
⇒ 2x + 3y – 9.35 = 0
⇒ 2x + 3y + (-9.35) = 0
Compare with ax + by + c = 0, we get
a = 2, b = 3, c = -9.35
(ii) x – y/5 – 10 = 0
⇒ 1 * x + (-1/5)y + (-10) = 0
Compare with ax + by + c = 0, we get
a = 1, b = -1/5, c = -10
(iii) –2x + 3y = 6
⇒ -2x + 3y – 6 = 0
⇒ -2x + 3y + (-6) = 0
Compare with ax + by + c = 0, we get
a = -2, b = 3, c = -6
(iv) x = 3y
⇒ x – 3y = 0
⇒ x + (-3)y + 0 = 0
Compare with ax + by + c = 0, we get
a = 1, b = -3, c = 0
Mddle block 1
(v) 2x = –5y
⇒ 2x + 5y = 0
⇒ 2x + 5y + 0 = 0
Compare with ax + by + c = 0, we get
a = 2, b = 5, c = 0
(vi) 3x + 2 = 0
⇒ 3x + 0*y + 2 = 0
Compare with ax + by + c = 0, we get
a = 3, b = 0, c = 0
(vii) y – 2 = 0
⇒ 0*x + 1*y + (-2) = 0
Compare with ax + by + c = 0, we get
a = 0, b = 1, c = -1
(viii) 5 = 2x
⇒ -2x + 5 = 8
⇒ -2x + 0 * y + 5 = 0
Compare with ax + by + c = 0, we get
a = -2, b = 0, c = 5