Elimination method of finding solution of a pair of LE

Q.

Find the solution of the following pair of equations.
$3x-5y=-1$ and $x-y=-1$

1. x = - 2 and y = - 1

2. x = 3 and y = - 1

3. x = - 1 and y = - 2

4. x = - 1 and y = - 4

Q. Sum of two numbers is 35 and their difference is 13. Find the greater number.

1. 21
2. 24
3. 26
4. 25

Q.

A modernistic painting consists of triangles rectangles and pentagons all drawn so as to not overlap or share sides within each rectangle are drawn $5$ red roses and each pentagon contains $4$ carnations.

How many triangles rectangles and pentagons appear in the painting iſ the painting contains a total of $38$ geometric figures $148$ sides of geometric figures, and $122$ flowers?

How many pentagons appear in the painting?​

Q.

The sum of the digits of a two digit number is $12$.

The number obtained by interchanging its digits exceed the given number by $18$.

Find the number.

Q.

Select the correct approach for solving a pair of linear equations in 2 variables by elimination method.
i) Add or subtract one equation from the other so that one variable gets eliminated.
ii) Multiply both the equations by any non-zero constant to make the coefficients of one variable (either x or y) numerically equal.
iii) Solve the equation in one variable (x or y) to get its value.
iv) Substitute the value of x (or y) in either of the original equations to get the value of the other variable.

1. (i), (iv), (ii), (iii)

2. (ii), (i), (iv), (iii)

3. (ii), (i), (iii), (iv)

4. (i), (ii), (iii), (iv)

Q.

In a parallelogram , one angle is $\frac{4}{5}$^th of its adjacent angle. Then the angles of the parallelogram are

1. 100, 80

2. 48, 60

3. 80, 64

4. 60, 75

Q.

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

1. 6, 4

2. 4, 6

3. 8, 12

4. None of these

Q. The sum of two numbers is 8. If their sum is four times their difference, find the numbers.

1. 5, 3
2. 7, 4
3. 10, 7
4. 9, 6

Q.

The solution of $\frac{x}{a}$ + $\frac{y}{b}$ = 1 and the $x$~ axis is ?

1. (-b, 0)

2. (-a, 0)

3. (b, 0)

4. (a, 0)

Q. A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If 5 is subtracted from the numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

1. $\frac{-7}{9}$
2. $\frac{7}{10}$
3. $\frac{-7}{10}$
4. None of the above

Q.

Two different equations can never have the same answer. State whether the statement is true (T) or false (F).

1. True
2. False

Q.

Find value of x in the given pair of equations.

$\frac{1}{x}+a=3$

$\frac{1}{x}-a=1$

1. $\frac{1}{2}$

2. 2

3. 4

4. $\frac{1}{4}$

Q. 4 chairs and 3 tables cost ₹ 2100 and 5 chairs and 2 tables cost ₹ 1750. Find the cost of a chair.

1. ₹ 200
2. ₹ 130
3. ₹ 150
4. ₹ 100

Q.

$3x–5y=4$
$9x=2y+7$

Solve the above equations by elimination method and find the value of x.

1. $x=\frac{9}{13}$

2. $x=\frac{5}{13}$

3. $x=\frac{-5}{13}$

4. $x=\frac{7}{13}$

Q.

$S_1$ : Sum of 5 consecutive odd numbers
$S_2$ : Sum of 4 consecutive even numbers

Sum of twice of $S_1$ and thrice of $S_2$ is 178. Also, thrice of $S_1$ and twice of $S_2$ is 177.

If all the 9 numbers are arranged in ascending order, the sum of the smallest and largest number is

1. 15

2. 16

3. 17

4. 18

Q.

Write an equation for the following questions:

a) $3$ times a number x is added to $5$ times another number y is equals to $48$.

b) Sum of squares of three number is $83$.

c) Difference of squares of two numbers m and n (m$>$n) is $56$.

d) A number divided by $5$ gives $7$ less than twice of the number.

Q.

Twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. Thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. Find the smallest even number.

1. 9

2. 11

3. 13

4. 15

Q.

Find value of $x$ in the given pair of equations.

$\frac{1}{x}+\frac{1}{y}=4$

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

1. $\frac{1}{3}$

2. $\frac{1}{6}$

3. 3

4. 6

Q.

$3x–4y=1$...(1)
$5x–6y=7$...(2)
In the above equations, which of the following step can to be done to numerically equate the coefficients of $x$?

1. Multiply equation (1) by 4 and equation (2) by 6.

2. Multiply equation (1) by 6 and equation (2) by 4.

3. Multiply equation (1) by 3 and equation (2) by 5.

4. Multiply equation (1) by 5 and equation (2) by 3.