Equations Reducible to a Pair of Linear Equation

Q. A motor boat can travel 30 km upstream and 28 km downstream in 7 h. It can travel 21 km upstream and return in 5 h. find the speed of the boat in still water and the speed of the stream.

Q. The sum of reciprocals of two number is $\frac{11}{30}$ and difference of reciprocals of two is $\frac{-1}{30}$. Find the two numbers.

1. 3 & 2
2. 5 & 6
3. 7 & 9
4. 11 & 13

Q.

Question 62

Write the number in the box , such that $\frac{3}{7}\times$ = $\frac{15}{98}.$

Q.

Question 49

A reciprocal of a fraction is obtained by inverting it upside down.

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. A motor boat can travel 30 km upstream and 28 km downstream in 7 h. It can travel 21 km upstream and return in 5 h. find the speed of the boat in still water and the speed of the stream.

Q.

Question 9

$\frac{1}{5}÷\frac{4}{5}$ is equal to

(a) $\frac{4}{5}$
(b) $\frac{1}{5}$
(c) $\frac{5}{4}$
(d) $\frac{1}{4}$

Q.

Question 112 (i)

Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1

The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?

Q. Find the values of $a\&b$ such that it satisfies following linear equations:
$\frac{4}{a+b}+\frac{2}{a-b}=5\frac{1}{a+b}+\frac{1}{a-b}=3$

1. $a=\frac{-11}{2}\&b=\frac{7}{20}$
2. $b=\frac{11}{2}\&a=\frac{-7}{20}$
3. $a=\frac{-8}{7}\&b=\frac{-6}{7}$
4. $b=\frac{6}{5}\&a=\frac{-8}{5}$

Q. The pair of equations 2x + 3y = 5 and 4x + 6y = 15 has ____
(a) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solution

Q. Question 6
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 us. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 min longer. Find the speed of the rickshaw and of the bus.

Q. The sum of reciprocals of two number is $\frac{11}{30}$ and difference of reciprocals of two is $\frac{-1}{30}$. Find the two numbers.

1. 5 & 6
2. 3 & 2
3. 7 & 9
4. 11 & 13

Q. The number of values of $k$ for which $\{x^2-(k-2)x+k^2\}+\{x^2+kx+(2k-1\left)\right\}$ is a perfect square is/are

1. $1$
2. none of these
3. $0$
4. $2$

Q. Find the value of x, y in the pair of equation given below, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

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

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

Q. Find the values of x and y in the below given pair of equation, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

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

Q.

Solve the following pair of linear equations.

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

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Here, x > 0 and y > 0.

1. x = 4, y = 9

2. x = 3, y = 2

3. x = 9, y = 8

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

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

1. Both A and B
2. $u=\frac{31}{22},v=\frac{23}{11}$
3. $u=0,v=0$
4. $u=\frac{22}{31},v=\frac{11}{23}$

Q. Find the value of x, y in the pair of equation given below, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

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