KSEEB SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1

KSEEB SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1.

Karnataka SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1

Question 1.
Aftab tells his daughter, “Seven years ago, I was, seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.
Solution:
Let the present age of father be x’
Let the age of daughter be ‘y’.
Before seven years, age of father is x – 7
Before seven years, age of daughter is y – 7.
Father was 7 times as old as daughter.
∴ x – 7 = 7 (y – 7)
x – 7 = 7y – 49
x – 7y = -49 + 7
x – 7y = – 42
∴ x – 7y + 42 = 0 …………….. (i)
After three years, age of father is x + 3
After three years, age of daughter is y + 3
Three years from now will three times as old as father.
∴ x + 3 = 3(y + 3)
x + 3 = 3y + 9
x – 3y + 3 – 9 = 0
3 – 3y – 6 = 0 ………….. (ii)
∴ Algebraically linear equations :
x – 7y + 42 = 0
x – 3y – 6 =0
If we represent this linear equations through graph, we have
i) x – 7y + 42 = 0
-7y = -x – 42
7y = x + 42
\(\quad y=\frac{x+42}{7}\)

x 0 7
\(y=\frac{x+42}{7}\) 6 7

ii) x – 3y – 6 = 0
-3y = -x + 6
3y = x – 6
\(\quad y=\frac{x-6}{3}\)

x 0 +6
\(y=\frac{x-6}{3}\) -2 0

KSEEB SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 1

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Question 2.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.
Solution:
Let the cost of a bat = ₹ x
and the cost of a ball = ₹ y
Cost of 3 bats = ₹ 3x
and cost of 6 balls = ₹ 6y
Again, cost of 1 bat = ₹ x
and cost of 3 balls = ₹ 3y
Algebraic representation:
Cost of 3 bats + Cost of 6 balls = ₹ 3900
⇒ 3x + 6y = 3900 ⇒ x + 2y = 1300 …. (1)
Also, cost of 1 bat + cost of 3 balls = ₹ 1300
⇒ x + 3y = 1300 …. (2)
Thus, (1) and (2) are the algebraic representations of the given situation.
Geometrical representation:
We have for equation (1),
KSEEB SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1
We can also see from the obtained graph that the straight lines representing the two equations intersect at (1300, 0).

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Question 3.
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and geometrically.
Solution:
Algebraically,
If Cost of each kg. of apple be Rs. ‘x’,
Cost of grapes be Rs. ‘y’. Then
2x + y = 160
4x + 2y = 300
To represent geometrically,
i) 2x + y = 160
y = -2x + 160

x 20 80
y = 2x + 160 120 0

ii) 4x + 2y = 300
2x + y= 150
y = 150 – 2x

x 40 60
y = 150 – 2x 70 30

KSEEB SSLC Class 10 Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 3
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