# KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.1

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## Karnataka Board Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.1

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. (Take the cost of a notebook to be Rs. x and that of a pen to be Rs. y).
Solution:
Let the cost of pen b Rs. x
If the cost of the Notebook is Rs. y.
Cost of 1 notebook is twice the cost of a pen.
∴ y = 2x
-2x + y = 0
If this is written in the form of
ax + by + c = 0 it is
-2x + y + 0 = 0
Here, a = -2, b = 1, c = 0.

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 . overline{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
viii) 5 = 2x
Solution:
i) 2x + 3y = (9 . overline{35})
OR 2x + 3y – (9 . overline{35}) = 0
If we compare this to ax + by + c = 0,
Here, a = 2, b = 3, c = (9 . overline{35}).

ii) x – (frac{y}{5}) – 10 = 0
If we compare this to ax + by + c = 0,
Here, a = 1, b = (frac{-1}{5}) , c=10.

iii) -2x + 3y = 6
OR -2x + 3y – 6 = 0
If we compare this to ax + by + c = 0,
Here, a = -2, b = 3, c = -6.

iv) x = 3y
x – 3y = 0
x – 3y + 0 = 0
If we compare this to ax + by + c = 0,
Here, a = 1, b = -3, c = 0.

v) 2x = -5y
2x + 5y = 0
2x + 5y + 0 = 0
If we compare this to ax + by + c = 0,
Here, a = 2, b = 5, c = 0.

vi) 3x + 2 = 0
3x + 0y + 2 = 0
If we compare this to ax + by + c = 0,
Here, a = 3, b = 0, c = 2.

vii) y – 2 = 0
0x + 1y – 2 = 0
If we compare this to ax + by + c = 0,
Here, a = 0, b = 1, c = -2.

viii) 5 = 2x
-2x + 5 = 0
-2x + 0y + 5 = 0
If we compare this to ax + by + c = 0,
Here, a = -2, b = 0, c = 5.

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