Gujarat Board GSEB Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1
Question 1.
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Solution:
Let the cost of a notebook be ₹ x and the cost of a pen be ₹ y.
Then according to the problem
x = 2y
⇒ x – 2y = 0
which is the required equation in two variables x and y.
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 – \(\frac {y}{5}\) – 10 = 0
(iii) -2x + 3y = 6
(iv) x = 3y
(v) 2x = -5y
(vi) 3x + 2 = 0
(vii) y – 2 = 0
(uiii) 5 = 2x
Solution:
(i) 2x + 3y = \(9 . \overline{35}\)
2x + 3y – \(9 . \overline{35}\) = 0
Comparing with the standard form of the equation, ax + by + c = 0, we get
a = 2, b = 3, c = – \(9 . \overline{35}\)
(ii) x – y – 10 = 0
1x + \(\left(\frac{-1}{5}\right)\)y + (-10) = 0
Comparing with the standard form of equation ax + by + c = 0, we get
a = 1, b = \(\left(\frac{-1}{5}\right)\), c = -10
(iii) -2x -3y = 6
(-2)x + 3y -6 = 0
(-2)x + 3y + (-6) = 0
Comparing with the standard form of equation ax + by + c = 0, we get
a = -2, b = 3, c = -6
(iv) x = 3y
x – 3y = 0
⇒ 1x + (-3)y + 0 = 0
Comparing with the standard form of equation
ax + by + c = 0, we get
a = 1, b = -3, c = 0
(v) 2x = -5y
2x + 5y + 0 = 0
Comparing with the standard form of equation
i.e., ax + by + c = 0, weget
a = 2, b = 5, c = 0
(vi) 3x + 2 = 0
3x + (0)y + 2 = 0
Comparing with the standard form of equation
ax + by + c = 0, we get
a = 3, b = 0, c = 2
y – 2 = 0
0x + ly + (-2) = 0
Comparing with the standard form of equation
ax + by + e = 0, we get
a = 3, b = 0, c = 2
(vii) y – 2 = 0
= 0x + ly + (-2) = 0
Comparing with the standard form of equation
ax + by + c = 0, we get
a = O, b = 1, c = -2
(viii) 5 = 2x
= -2x + 5 = 0
(-)x + (0)y + 5 = 0
Comparing with the standard form of equation
ax + by + c = 0, we get
a = -2, b = 0, c = 5