Solving Simultaneous Linear Equation Using Method of Elimination

Q. A boat goes 30 km upstream and 44 downstream in 10 hours. The same boat goes 40 km upstream and 55 km downstream in 13 hours. On this information some student guessed the speed of the boat in still water as 8.5 km/h and speed of the boat in still water as 8.5 km/h and speed of the stream as 3.8 km/h. Do you agree with their guess?
Explain what do we learn from the incident?

Q. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.

1. 44 km/hr, 8 km/hr
2. 6 km/hr, 4 km/hr
3. 10 km/hr, 2 km/hr
4. 14 km/hr, 5 km/hr

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.

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. (12, 8)

Q.

Solve the equations $3x–y=5,x+3y=5$

1. 1, 2

2. 2, 1

3. -1, -1

4. -2, -2

Q.

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11 hours more than earlier.
Find the speed of the stream and speed of the boat.

1. 4, 7

2. 7, 8

3. 3, 2

4. 6, 3

Q.

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km then total time taken increases by 11 hours. Find the speed of the stream and speed of the boat.

1. 4, 7

2. 7, 8

3. 3, 2

4. 6, 3

Q. A man starts his job with a certain salary and earns a fixed increment every year. If his salary was ₹15000 after 4 years of service and ₹18000 after 10 years of service, then find his starting salary and annual increment respectively.

1. ₹11000, ₹700
2. ₹13000, ₹500
3. ₹13000, ₹700
4. ₹11000, ₹500

Q.

If $l\left(my+nz-lx\right)=m\left(nz+lx-my\right)=n\left(lx+my-nz\right)$, prove $\frac{\left(y+z-x\right)}{l}=\frac{\left(z+x-y\right)}{m}=\frac{\left(x+y-z\right)}{n}$.

Q.

Write equation for the following statement:

The difference of $y$ and $2$ is $8$

Q. In a movie theatre seating 625 people, the number of rows in front of Sheila is thrice the number of rows behind her. Also, the number of seats to her left is twice the number of seats to her right. Find where Sheila is sitting.

(There are as many seats in a row as there are rows in total. Count the rows from the front to the back and the seats from the left to the right with respect to Sheila.)

1. 17th seat in the 19th row
2. 18th seat in the 16th row
3. 19th seat in the 17th row
4. 16th seat in the 18th row

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.

It takes 14 hr to travel 30km in upstream and 44 km in downstream. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km then total time taken is 11hr more than earlier. Find the speed of stream and speed of boat.

1. 4, 7

2. 7, 8

3. 3, 2

4. 6, 3

Q.

The time taken to travel 30 km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11 km then the total time taken is 11 hours more than earlier. Find the speed of the stream.

1. 4 km/hr

2. 7 km/hr

3. 3 km/hr

4. 6 km/hr

Q.

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11 hours more than earlier.
Find the speed of the stream and speed of the boat.

1. 4, 7

2. 7, 8

3. 3, 2

4. 6, 3

Q.

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

1. 34

2. 32

3. 30

4. 24

Q.

Find the value of x?

x + y = 5
3x - y = 3

1. -2

2. 2

3. 3

4. -3

Q.

Find the value of y?
x + y = 1 and -x + y = -3

1. -2

2. -1

3. 2

4. 1

Q.

Solve the following pair of equations and choose the correct answer.
2x + y = 7
3x + 2y = 12

1. (2, 3)

2. (-3, 2)

3. (1, 0)

4. (3, 2)

Q. A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If, however, 5 is subtracted from 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. $\frac{-7}{9}$

Q. The sum of numerator and denominator of a fraction is $3$ less than twice the denominator.If each of the numerator and denominator is decrease by $1$, the fraction becomes $\frac{1}{2}$.Find the fraction.

Q.

If the numerator of a fraction is increased by 2 and its denominator is decreased by 1, it becomes $\frac{2}{3}$. If the numerator is increased by 1 and the denominator is increased by 2, it becomes $\frac{1}{3}$. Find the fraction.

1. $x=3andy=7$

2. $x=2andy=7$

3. $x=2andy=6$

4. $x=-2andy=-7$

Q. In the method of cross multiplication, a pair of linear equations in 2 variables can be solved just by multiplying the equations.

1. False
2. True

Q.

Find the solution of the given pair of equations
$2x+3y=9,3x+4y=5$

1. x = 21, y = 7

2. x = - 21, y = 17

3. x = 19, y = 14

4. x = 20, y = 12

Q. Solve for $x$ and $y$:
$\frac{5}{x}+6y=13\frac{3}{x}+4y=7(x\ne 0)$

Q. The sum of the numerator and the denominator of a fraction is equal to $7$. Four times the numerator is $8$ less than $5$ times the denominator. Find the fraction.

1. $\frac{1}{6}$
2. $\frac{3}{4}$
3. $\frac{4}{7}$
4. $\frac{7}{11}$

Q. In covering a distance of $30km$. Amit takes $2hrs.$ more than suresh. If Amit doubles his speed, he would take one hour less than suresh. Amit's speed is

1. $5km/hr$
2. $7.5km/hr$
3. $6km/hr$
4. $6.25km/hr$

Q. When $3$ is added to the denominator and $2$ is subtracted from the numerator a fraction becomes $\frac{1}{4}$. And, when $6$ is added to numerator and the denominator is multiplied by $3$, it becomes $\frac{2}{3}$. Find the fraction.

Q.

Find the values of $x$ and $y$ if :

$\frac{5}{2+x}+\frac{1}{y-4}=2$

$\frac{6}{2+x}-\frac{3}{y-4}=1$

Here, x $\ne$ -2 and y $\ne$ 4.

1. x = -2, y = 2

2. x = 0, y = 8

3. x = 7, y = -8

4. x = 1, y = 7

Q.

A man starts his job with a certain salary and earns a fixed increment every year. If his salary was ₹ 15000 after 4 years of service and ₹ 18000 after 10 years of service, then find his starting salary and annual increment respectively.

1. ₹ 11000, ₹ 700

2. ₹ 13000, ₹ 500

3. ₹ 11000, ₹ 500

4. ₹ 13000, ₹ 700