Method of Substitution

Q.

In a two-digit number, the units digit is twice the ten's digit. If $27$ is added to the number, the digits are reversed. Find the number.

1. $40$

2. $52$

3. $928$

4. $36$

Q. The sum of the digits of a two-digit number is 9. If 9 is added to the number obtained by reversing the digits of this number, the result is 3 times the original number. Find the number.

1. 27
2. 36
3. 81
4. 45

Q.

The pairs of linear equations whose solution is x = 2, y = –3 are

1. x + y = –1 ; 2x – 3y = –5

2. 2x + 5y = –11 ; 4x + 10y = –22

3. 2x – y = 1 ; 3x + 2y = 0

4. x – 4y –14 = 0 ; 5x – y – 13 = 0

Q. If x + 3y = 6 and 2x - 3y = 12, then the value of $(x-y{)}^2$ is:

1. 16
2. 25
3. 36
4. 49

Q.

Solving $\frac{5}{2+x}$ + $\frac{1}{y-4}$ = 2; $\frac{6}{2+x}$ - $\frac{3}{y-4}$ = 1,
we get
x = ___
y = ___

Q.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. [4 MARKS]

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. 25
2. 24
3. 26
4. 27

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

Q.

Sum of two numbers is 4 more than twice of difference of the two numbers. If one of the two numbers is three more than the other number, find the numbers.

1. ( , 3)

2. (, )

3. (1, 3)

4. (1, 2)

Q. $2$ women and $5$ men can together finish an embroidery work in $4$ days, while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ woman alone to finish the work, and also that taken by $1$ man alone.

Q.

The line 6x + 5y = 9, cuts the x-axis at

1. ( , 0)

2. (1, )

3. (0, )

4. (2, 3)

Q.

The sum of two numbers is 4 more than twice their difference. One of the two numbers is three more than the other number. Find the numbers.

1. (1, 3)

2. (, )

3. ( , 3)

4. (1, 2)

Q.

54 is divided into 2 parts such that the sum of 10 times the first part and 22 times the second part is 780. The bigger number is ----

1. 34

2. 32

3. 24

4. 30

Q.

One angle of a parallelogram is twice the adjacent angle. Form the linear equations in two variables and find the measures of angles of the parallelogram.

1. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$

2. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$

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

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

Q. Question 2 (iii)
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.
6x – 3y + 10 = 0
2x – y + 9 = 0

Q.

Solve the following equations:
$8v-3u=5uv$
$6v-5u=-2uv$

1. 
2. 
3. Both A and B
4. None of these

Q.

The value of $y$ in the following pair of equations is ___

$x+y=7$

$5x+12y=7$

Q.

From the pair of linear equations in the following problems and find their solutions graphically.

The ages of two girls are in the ratio 5:7.Eight years ago their ages were in the ratio 7:13. Find their present ages

Q.

The given statements are the steps to be followed in the method of substitution in random order. Arrange them in correct order to solve two equations

1) Find the value of one variable, say y in terms of x if x and y are the two variables

2) Substitute the value of x obtained from previous step in either of the equation to find y.

3) Substitute y in the second equation and it will be reduced to an equation in x, find x

1. 1, 2, 3

2. 1, 3, 2

3. 2, 3, 1

4. 3, 2, 1

Q.

Find the value of k if (1, 3k) lies on kx + 4y = 26

1. 1

2. 0

3. 2

4. 4

Q.

In an examination, the ratio of passes to failures was 4:1. Had 30 less appeared , and 20 less passed, the ratio of passes to failures would have been 5:1.Represent this situation algebraically and graphically

Q.

The linear equation 2x – 5y = x – 2 has

1. No solution

2. One solution

3. Two solutions

4. Infinitely many solutions

Q.

₹ 9, 000 was divided equally among a certain number of people. Had there been 20 more people, each would have got ₹ 160 less. Find the number of people.

1. 24

2. 25

3. 26

4. 27

Q.

If f(x+2y, x-2y)=xy, then f(x, y) equals

1. 
2. 
3. 
4. 

Q. Solve the following systems of equations:
$99x+101y=499$
$101x+99y=501$

Q. A and B together finish a piece of work in 6 days. If A’s one day’s work is two times that of B, the number of days A and B take to finish the work alone is ____ and ____ respectively.

1. 9, 18
2. 12, 24
3. 7, 14
4. 8, 16

Q. Solve the following systems of equations:
$23x-29y=98$
$29x-23y=110$

Q.

Does representing equation y =x+3 pass through original?why or why not ?

Regards😌

Q. 12 men can do a work in 9 days. If 6 more men are engaged to do the same work, then how long will it take to complete the same work?

1. 8 days
2. 6 days
3. 4 days
4. 5 days

Q.

The statements given below are the steps that need to be followed in the method of substitution in random order. Arrange them in correct order to solve two equations.

1) Find the value of one variable, say y in terms of the x if x and y are the two variables.

2) Substitute the x we got from step 2 in either of the equation to get y.

3) Substitute this y in the second equation and it will be reduced to an equation in x, find x.

1. 1, 2, 3

2. 1, 3, 2

3. 2, 3, 1

4. 3, 2, 1