Substitution Method to Find the Solution of Pair of Linear Equations

Q.

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 8. Find the number.

Q. Question 2 (i)
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?

Q. In a two-digit number, the units digit is twice the tens digit. If 9 is added to the number, the digits interchange their places. Find the number.

1. 45
2. 12
3. 21
4. 54

Q. Seema has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 75 and the amount of money with her is ₹100, then the number of ₹1 and ₹2 coins respectively are

1. 50 and 25
2. 25 and 50
3. 60 and 15
4. 35 and 50

Q.

Write the expression of:-

$30$ less than twice the sum of $xandy$

Q.

Sum of digits of a 2 digit number is 10. Sum of the number and its reverse equals 110. Represent it graphically.

1. 

2. 

3. 

4. 

Q.

Write the expression of:-

Add $y$ to the product of $xandz$

Q. Question 2
Write four solutions for each of the following equations:
$\left(i\right)2x+y=7\left(ii\right)\pi x+y=9\left(iii\right)x=4y$

Q.

Q.

Question 2 (i)
On comparing the ratios $\frac{a_1}{a_2}$ , $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
5x - 4y + 8 = 0
7x + 6y - 9 = 0

Q. Places A and B are 200 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
[Substitution Method] [ 2 marks ]

Q. Solve the following pair of linear equations by substitution method: 𝟐𝒙 − 𝟑𝒚 = 𝟓 and 𝟑𝒙 + 𝟐𝒚 = 𝟏𝟒

Q. Find the value of $x$ and $y$ if :

1. x = 2, y = 3
2. x = 1, y = 1
3. x = 2, y = 0
4. x = 4, y = -1

Q. Solve:
$x-2y=0and3x-y=5$

1. $x=2,y=2$
2. $x=2,y=1$
3. $x=2,y=4$
4. $x=1,y=2$

Q. If the numerator is decreased by 1 and denominator is multiplied by 2, then the resulting fraction is $\frac{1}{5}$.If the numerator is increased by 12 and denominator is multiplied by 6, then the resulting fraction is $\frac{1}{2}$. What is the difference between the numerator and the denominator?

1. 1
2. -2
3. 3
4. -5

Q.

The value of a for which the lines $x=1$, $y=2$ and $a^{2}x+2y-20=0$ are concurrent is:

1. 1

2. 4

3. -1

4. -2

Q. What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(Where $x\ne 0,y\ne 0)$

Q.

Suppose you are $y$ years old and your mother is $m$ years old.

Write in mathematical form the statement that “your mother is more than twice as old as you”.

Q.

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?

1. 2 m, 20 m

2. 26 m, 20 m

3. 56 m, 40 m

4. 2 m, 3 m

Q. The father’s age is six times his son’s age. Four years from now, the age of the father will be four times his son’s age. The present ages (in years) of the father and the son respectively are ___.

1. 60 years, 10 years
2. 36 years, 6 years
3. 30 years, 5 years
4. 24 years, 4 years

Q.

Measure of one of the angles of a parallelogram is twice the measure of its adjacent angle. Then angles of the parallelogram are

1. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$

2. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$

3. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$

4. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$

Q. A sum of ₹ 9, 000 was divided equally among a certain number of people. If there are 20 more people, each would have got Rs. 160 less. Find the original number of people.

1. 24
2. 25
3. 26
4. 27

Q. Solve :
$2x-3y=2,x+2y=8$
using the method of substitution.

1. $x=-4,y=-2$
2. $x=2,y=4$
3. $x=4,y=2$
4. $x=6,y=2$

Q.

Write two solutions of the form: $x=0$, $y=a$ and $x=b$, $y=0$ for $5x-2y=10$

Q.

The difference between $72$ and $16$?

Q. What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(Given: $x\ne 0andy\ne 0)$

Q. Find x and y if $\frac{1}{x-1}+\frac{4}{y+1}=-2and\frac{3}{x-1}-\frac{1}{y+1}=7$

1. (2, 0)
2. (0, 2)
3. $(\frac{3}{2},-2)$
4. $(-\frac{3}{2},2)$

Q. What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(Given: $x\ne 0andy\ne 0)$

Q.

Solve the equations for $x$ and $y$.

$2x-3y=7$

$5x+y=9$

1. 3, 4

2. 2, -1

3. 2, 2

4. 3, -1