Elimination Method

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. ₹ 100
4. ₹ 150

Q. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.

1. 40 km/hr, 10 km/hr
2. 10 km/hr, 30 km/hr
3. 10 km/hr, 40 km/hr
4. 30 km/hr, 10 km/hr

Q.

Three consecutive integers are such that when they are taken in increasing order and multiplied by $2,3and4$ respectively, they add up to $74$. Find these numbers.

Q. If 3x - y = 7 and 2x + 5y = - 1, then the values of x and y are

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

Q. Solve the following pair of equations:

$7x-8y=-12$

$-4x+2y=3$

1. $x=0,y=0$
2. $x=0,y=\frac{3}{2}$
3. $x=\frac{5}{2},y=4$
4. $x=6,y=\frac{1}{2}$

Q.

At a closing down sale, a book store was selling 3 books and 5 notebooks for Rs 309 or 6 books and 2 notebooks for Rs 282. How much would one book and 1 notebook cost?

1. 33

2. 57

3. 75

4. 42

Q.

Rohan spends ₹ $x$ daily and saves ₹ $y$ per week. What is his income for $3$ weeks?

Q.

The cost of 3 books and 5 notebooks is Rs 250, while the cost of 4 books and 4 notebooks is Rs 280.

If the cost of a book is represented by x and the cost of a notebook is represented by y, then which set of equations represents the given information?

1. 3x + 5y = 250 4x + 4y = 280

2. 5x + 4y = 250 3x + 4y = 280

3. 4x + 5y = 250 4x + 3y = 280

4. 5x + 3y = 250 4x + 4y = 280

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

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

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

Q.

The multiplication of two integers is $256$. If one of them is $32$, determine the other.

Q. The ratio of Sam's and Rahul's income is 5:4 and the ratio of their expenditures is 3:2. If at the end of the year each saves ₹1600, then Sam's income is

1. ₹1600
2. ₹2400
3. ₹3200
4. ₹4000

Q. Solve the following simultaneous equations: $\frac{x}{3}+5y=13$ and $2x+\frac{y}{2}=19$

1. $x=2$, $y=9$
2. $x=-2$, $y=-9$
3. $x=9$, $y=2$
4. $x=-2$, $y=9$

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. If $3x+5y=9$ and $5x+3y=7$ then what is the value of $x+y$?
$\left[4\right]$
[4 Marks]

Q.

Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. [4 MARKS]

Q.

A leading library has fixed charge for the first three days and an additional charges for each day thereafter. Johan paid 25rupees for a book kept for seven days. If the fixed charges be rupees X and subsequent per day charges be rupees Y; then write the linear equation representing the above information and draw the graph of the same. From the graph if the fixed charge is 7 rupees, find the subsequent per day charge. And if the per day charge 4rupees, find the fixed charge(charge is 7 rupees)

Q. A number is 27 more than the number obtained by reversing it's digits.if it's ones place is x and tens digit y.Write a linear linear equation representing the above statement

Q. The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

1. ₹120, ₹48/hr
2. ₹120, ₹100/hr
3. ₹200, ₹48/hr
4. ₹200, ₹120/hr

Q.

Rafiq starts his job with a salary of rs 80, 000 per year. he earns an increment of rs 5, 000 every year. if his yearly salary after x years is rs y , then show the equation that correctly relates x and y.

Q.

Why do we multiply a constant if it is given as a no. A is inversely proportional to B then , A= KB (where K is constant)?

Q.

The sum of two integers is $-89$. If one of them is $17$, find the other.

Q.

Find the values of x and y in the given pair of equations.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

1. $\frac{1}{2}$, $\frac{1}{3}$

2. $\frac{1}{3}$, $\frac{1}{2}$

3. 2, 3

4. 3, 2

Q. The solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13 is ________.

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

Q. Solve the following system of linear equations by using the method of elimination by equating the coefficients
$\sqrt{3}x-\sqrt{2}y=\sqrt{3};\sqrt{5}x+\sqrt{3}y=\sqrt{2}$
[3 Marks]

Q.

Find the unique solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13.

1. (1, 2)

2. (2, 1)

3. (3, 1)

4. (1, 3)

Q. Half the perimeter of a rectangular garden, whose length is 8 m more than its width, is 40 m. Find the dimensions of the garden.

1. Length = 20m, Breadth = 18m
2. Length = 24m, Breadth = 20m
3. Length = 40m, Breadth = 36m
4. Length = 24m, Breadth = 16m

Q. Question 1 (iv)
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
x - 3y - 7 = 0 ; 3x - 3y - 15= 0

Q.

The pairs of linear equations which have the unique solution 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. Evaluate for $x$ and $y$

Q.

In the elimination method --------- is a must.

1. Equating both the co-efficients

2. Equating only the x co-efficient

3. Equating only the y co-efficient

4. Equating either of the co-efficients