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02 - Question Bank - Pair Of Linear Equations - Class 10 - Maths Class 10 Notes | EduRev

Class 10 : 02 - Question Bank - Pair Of Linear Equations - Class 10 - Maths Class 10 Notes | EduRev

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PAIR OF LINEAR EQUATION ALGEBRAICALLY AND GRAPHICALLY
1) Maria tells her son “Five years ago, I was two times as old as you were then. Also two years from now,
I shall be two times as old as you will be”. Represent this situation algebraically and graphically.
Solution:
Step1:
Let Maria’s and her son’s present age be ‘x’ years and ‘y’ years respectively.
Step2:
Five years ago
Maria’s age was(x – 5) years
Her Son’s age was (y-5) years
Step3:
Two years later
Maria’s age will be(x + 2) years
Her son’s age will be (y + 2) years
Step4:
Given,   5 years ago Maria’s age = 2 times her son’s age then
?
) 5 ( 2 5 ? ? ? y x

? 0 5 2 ? ? ? y x

Step5:
Given, 2 years hence, Maria’s age = 2 times her son’s age then,
? ) 2 ( 2 2 ? ? ? y x

? 0 2 2 ? ? ? y x

Thus, algebraic representation of the given situations is
0 5 2 ? ? ? y x ………. (I)
0 2 2 ? ? ? y x ………… (II)
Step6:
To obtain equivalent graphical representation we find two points on the line representing each equation.
That is we find two solutions of each equation.
Now,     2 2 ? ? y x ……………… FROM (II)
?
2
2 ?
?
x
y

Therefore, 0 ? x ? 1
2
2 0
? ?
?
? y

2 ? x ? 0
2
2 2
?
?
? y

Thus, the two solutions of the equation 0 2 2 ? ? ? y x are:
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Page 2

PAIR OF LINEAR EQUATION ALGEBRAICALLY AND GRAPHICALLY
1) Maria tells her son “Five years ago, I was two times as old as you were then. Also two years from now,
I shall be two times as old as you will be”. Represent this situation algebraically and graphically.
Solution:
Step1:
Let Maria’s and her son’s present age be ‘x’ years and ‘y’ years respectively.
Step2:
Five years ago
Maria’s age was(x – 5) years
Her Son’s age was (y-5) years
Step3:
Two years later
Maria’s age will be(x + 2) years
Her son’s age will be (y + 2) years
Step4:
Given,   5 years ago Maria’s age = 2 times her son’s age then
?
) 5 ( 2 5 ? ? ? y x

? 0 5 2 ? ? ? y x

Step5:
Given, 2 years hence, Maria’s age = 2 times her son’s age then,
? ) 2 ( 2 2 ? ? ? y x

? 0 2 2 ? ? ? y x

Thus, algebraic representation of the given situations is
0 5 2 ? ? ? y x ………. (I)
0 2 2 ? ? ? y x ………… (II)
Step6:
To obtain equivalent graphical representation we find two points on the line representing each equation.
That is we find two solutions of each equation.
Now,     2 2 ? ? y x ……………… FROM (II)
?
2
2 ?
?
x
y

Therefore, 0 ? x ? 1
2
2 0
? ?
?
? y

2 ? x ? 0
2
2 2
?
?
? y

Thus, the two solutions of the equation 0 2 2 ? ? ? y x are:
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Step7:
Plot the points A (0,-1) and B (2, 0) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 0 2 2 ? ? ? y x

Step8:
Also, consider 0 5 2 ? ? ? y x

?
2
5 ?
?
x
y

Therefore, 1 ? x ? 3
2
5 1
?
?
? y

3 ? x ? 4
2
5 3
?
?
? y

Thus, the two solutions of the equation 0 5 2 ? ? ? y x are:
x 1 3
y
3 4

Step9:
Plot the points P(1,3) and Q(3,4) on the same graph paper.
Draw a line passing through the point P and Q.
Then the PQ represents the equation 0 5 2 ? ? ? y x

We observe that line do not intersect anywhere.

x 0 2
y
-1 0
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Page 3

PAIR OF LINEAR EQUATION ALGEBRAICALLY AND GRAPHICALLY
1) Maria tells her son “Five years ago, I was two times as old as you were then. Also two years from now,
I shall be two times as old as you will be”. Represent this situation algebraically and graphically.
Solution:
Step1:
Let Maria’s and her son’s present age be ‘x’ years and ‘y’ years respectively.
Step2:
Five years ago
Maria’s age was(x – 5) years
Her Son’s age was (y-5) years
Step3:
Two years later
Maria’s age will be(x + 2) years
Her son’s age will be (y + 2) years
Step4:
Given,   5 years ago Maria’s age = 2 times her son’s age then
?
) 5 ( 2 5 ? ? ? y x

? 0 5 2 ? ? ? y x

Step5:
Given, 2 years hence, Maria’s age = 2 times her son’s age then,
? ) 2 ( 2 2 ? ? ? y x

? 0 2 2 ? ? ? y x

Thus, algebraic representation of the given situations is
0 5 2 ? ? ? y x ………. (I)
0 2 2 ? ? ? y x ………… (II)
Step6:
To obtain equivalent graphical representation we find two points on the line representing each equation.
That is we find two solutions of each equation.
Now,     2 2 ? ? y x ……………… FROM (II)
?
2
2 ?
?
x
y

Therefore, 0 ? x ? 1
2
2 0
? ?
?
? y

2 ? x ? 0
2
2 2
?
?
? y

Thus, the two solutions of the equation 0 2 2 ? ? ? y x are:
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Step7:
Plot the points A (0,-1) and B (2, 0) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 0 2 2 ? ? ? y x

Step8:
Also, consider 0 5 2 ? ? ? y x

?
2
5 ?
?
x
y

Therefore, 1 ? x ? 3
2
5 1
?
?
? y

3 ? x ? 4
2
5 3
?
?
? y

Thus, the two solutions of the equation 0 5 2 ? ? ? y x are:
x 1 3
y
3 4

Step9:
Plot the points P(1,3) and Q(3,4) on the same graph paper.
Draw a line passing through the point P and Q.
Then the PQ represents the equation 0 5 2 ? ? ? y x

We observe that line do not intersect anywhere.

x 0 2
y
-1 0
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

2. A shopkeeper sold 4 chocolates and 5 lollipops for Rs 8 to a customer. A little lateranothercustomer
purchased 5 chocolates and 5 lollipops for Rs 10. Represent the situation algebraically and graphically.
Solution:
Step 1:
Let the price of chocolate be Rsx , and that of lollipop be Rs y .
Given, 4 chocolates and 5 lollipops were purchased for Rs 8.
Step2: 8 5 4 ? ? ? y x

Given, 5 chocolates and 5 lollipops were purchased for Rs 10.
Step3: 10 5 5 ? ? ? y x

Then the algebraic representation of the given situation is
) .( .......... .......... 8 5 4 I y x ? ?

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Page 4

PAIR OF LINEAR EQUATION ALGEBRAICALLY AND GRAPHICALLY
1) Maria tells her son “Five years ago, I was two times as old as you were then. Also two years from now,
I shall be two times as old as you will be”. Represent this situation algebraically and graphically.
Solution:
Step1:
Let Maria’s and her son’s present age be ‘x’ years and ‘y’ years respectively.
Step2:
Five years ago
Maria’s age was(x – 5) years
Her Son’s age was (y-5) years
Step3:
Two years later
Maria’s age will be(x + 2) years
Her son’s age will be (y + 2) years
Step4:
Given,   5 years ago Maria’s age = 2 times her son’s age then
?
) 5 ( 2 5 ? ? ? y x

? 0 5 2 ? ? ? y x

Step5:
Given, 2 years hence, Maria’s age = 2 times her son’s age then,
? ) 2 ( 2 2 ? ? ? y x

? 0 2 2 ? ? ? y x

Thus, algebraic representation of the given situations is
0 5 2 ? ? ? y x ………. (I)
0 2 2 ? ? ? y x ………… (II)
Step6:
To obtain equivalent graphical representation we find two points on the line representing each equation.
That is we find two solutions of each equation.
Now,     2 2 ? ? y x ……………… FROM (II)
?
2
2 ?
?
x
y

Therefore, 0 ? x ? 1
2
2 0
? ?
?
? y

2 ? x ? 0
2
2 2
?
?
? y

Thus, the two solutions of the equation 0 2 2 ? ? ? y x are:
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Step7:
Plot the points A (0,-1) and B (2, 0) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 0 2 2 ? ? ? y x

Step8:
Also, consider 0 5 2 ? ? ? y x

?
2
5 ?
?
x
y

Therefore, 1 ? x ? 3
2
5 1
?
?
? y

3 ? x ? 4
2
5 3
?
?
? y

Thus, the two solutions of the equation 0 5 2 ? ? ? y x are:
x 1 3
y
3 4

Step9:
Plot the points P(1,3) and Q(3,4) on the same graph paper.
Draw a line passing through the point P and Q.
Then the PQ represents the equation 0 5 2 ? ? ? y x

We observe that line do not intersect anywhere.

x 0 2
y
-1 0
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

2. A shopkeeper sold 4 chocolates and 5 lollipops for Rs 8 to a customer. A little lateranothercustomer
purchased 5 chocolates and 5 lollipops for Rs 10. Represent the situation algebraically and graphically.
Solution:
Step 1:
Let the price of chocolate be Rsx , and that of lollipop be Rs y .
Given, 4 chocolates and 5 lollipops were purchased for Rs 8.
Step2: 8 5 4 ? ? ? y x

Given, 5 chocolates and 5 lollipops were purchased for Rs 10.
Step3: 10 5 5 ? ? ? y x

Then the algebraic representation of the given situation is
) .( .......... .......... 8 5 4 I y x ? ?

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

) ( .......... .......... 10 5 5 II y x ? ?

Geometric/ graphical representation
Step4:
To obtain the equivalent graphical representation, we find two points on the line representing each equation,
that is, we find two solution of each equation.
Now,
) .( .......... .......... 8 5 4 FromI y x ? ?

5
4 8 x
y
?
? ?

Therefore, 2 ? x 0
5
2 4 8
?
? ?
? ? y

2 ? ? x 2 . 3
5
16
5
)] 2 ( 4 [ 8
? ?
? ? ?
? ? y

Thus, the two solutions of the equation 8 5 4 ? ? y x are:
x 2 -2
y
0 3.2
Step5:
Plot the point A (2, 0) and B (-2, 3.2) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 8 5 4 ? ? y x .
Step6:
Now, ) ( .... .......... 10 5 5 II From y x ? ?

5
5 10 x
y
?
? ?
Therefore, 2 ? x 0
5
2 5 10
?
? ?
? ? y
2 ? ? x
4
5
20
5
)] 2 ( 5 [ 10
? ?
? ? ?
? ? y

Thus, the two solutions of the equation 10 5 5 ? ? y x are:
x 2 -2
y
0 4

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Page 5

PAIR OF LINEAR EQUATION ALGEBRAICALLY AND GRAPHICALLY
1) Maria tells her son “Five years ago, I was two times as old as you were then. Also two years from now,
I shall be two times as old as you will be”. Represent this situation algebraically and graphically.
Solution:
Step1:
Let Maria’s and her son’s present age be ‘x’ years and ‘y’ years respectively.
Step2:
Five years ago
Maria’s age was(x – 5) years
Her Son’s age was (y-5) years
Step3:
Two years later
Maria’s age will be(x + 2) years
Her son’s age will be (y + 2) years
Step4:
Given,   5 years ago Maria’s age = 2 times her son’s age then
?
) 5 ( 2 5 ? ? ? y x

? 0 5 2 ? ? ? y x

Step5:
Given, 2 years hence, Maria’s age = 2 times her son’s age then,
? ) 2 ( 2 2 ? ? ? y x

? 0 2 2 ? ? ? y x

Thus, algebraic representation of the given situations is
0 5 2 ? ? ? y x ………. (I)
0 2 2 ? ? ? y x ………… (II)
Step6:
To obtain equivalent graphical representation we find two points on the line representing each equation.
That is we find two solutions of each equation.
Now,     2 2 ? ? y x ……………… FROM (II)
?
2
2 ?
?
x
y

Therefore, 0 ? x ? 1
2
2 0
? ?
?
? y

2 ? x ? 0
2
2 2
?
?
? y

Thus, the two solutions of the equation 0 2 2 ? ? ? y x are:
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Step7:
Plot the points A (0,-1) and B (2, 0) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 0 2 2 ? ? ? y x

Step8:
Also, consider 0 5 2 ? ? ? y x

?
2
5 ?
?
x
y

Therefore, 1 ? x ? 3
2
5 1
?
?
? y

3 ? x ? 4
2
5 3
?
?
? y

Thus, the two solutions of the equation 0 5 2 ? ? ? y x are:
x 1 3
y
3 4

Step9:
Plot the points P(1,3) and Q(3,4) on the same graph paper.
Draw a line passing through the point P and Q.
Then the PQ represents the equation 0 5 2 ? ? ? y x

We observe that line do not intersect anywhere.

x 0 2
y
-1 0
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

2. A shopkeeper sold 4 chocolates and 5 lollipops for Rs 8 to a customer. A little lateranothercustomer
purchased 5 chocolates and 5 lollipops for Rs 10. Represent the situation algebraically and graphically.
Solution:
Step 1:
Let the price of chocolate be Rsx , and that of lollipop be Rs y .
Given, 4 chocolates and 5 lollipops were purchased for Rs 8.
Step2: 8 5 4 ? ? ? y x

Given, 5 chocolates and 5 lollipops were purchased for Rs 10.
Step3: 10 5 5 ? ? ? y x

Then the algebraic representation of the given situation is
) .( .......... .......... 8 5 4 I y x ? ?

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

) ( .......... .......... 10 5 5 II y x ? ?

Geometric/ graphical representation
Step4:
To obtain the equivalent graphical representation, we find two points on the line representing each equation,
that is, we find two solution of each equation.
Now,
) .( .......... .......... 8 5 4 FromI y x ? ?

5
4 8 x
y
?
? ?

Therefore, 2 ? x 0
5
2 4 8
?
? ?
? ? y

2 ? ? x 2 . 3
5
16
5
)] 2 ( 4 [ 8
? ?
? ? ?
? ? y

Thus, the two solutions of the equation 8 5 4 ? ? y x are:
x 2 -2
y
0 3.2
Step5:
Plot the point A (2, 0) and B (-2, 3.2) on a graph paper.
Draw a line passing through the points A and B.
Then, the line AB represents the equation 8 5 4 ? ? y x .
Step6:
Now, ) ( .... .......... 10 5 5 II From y x ? ?

5
5 10 x
y
?
? ?
Therefore, 2 ? x 0
5
2 5 10
?
? ?
? ? y
2 ? ? x
4
5
20
5
)] 2 ( 5 [ 10
? ?
? ? ?
? ? y

Thus, the two solutions of the equation 10 5 5 ? ? y x are:
x 2 -2
y
0 4

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Step7:
Plot the point P (2, 0) and Q (-2, 4), on the same graph.
Draw a line passing through the points P and Q.

Then, the line PQ represents the equation 10 5 5 ? ? y x

From the graph we observe that, the two lines representing the situation graphically, intersect at(2,0)

GRAPHICAL METHOD OF SOLVING LINEAR EQUATIONS

3) 9 students of Class 8 took part in a Science Quiz. If the number of boys is 5 more than
the number of girls, find the number of boys and girls who took part in the quiz.
Solution:

X axis- 1cm = 1 unit
Y axis- 1cm = 1unit
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Mathematics (Maths) Class 10

51 videos|346 docs|103 tests

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