Equations Reducible to a Pair of Linear Equation

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. 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. 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. 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. 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. 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. 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. $x=3,y=2$

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.

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