Eqns. reducible to pair of LE in 2 variables

Q.

$A$ takes $3$ hour more than $B$ to walk $30km$. But if $A$ doubles his pace, he is ahead of $B$ by $\frac{3}{2}hours$. Find their speed of walking.

Q. Solve the following equation and check your results:
$2y+\frac{5}{3}=\frac{26}{3}-y$

Q. Solve the equation:
$14y-8=13$

Q. Question 9 (vii)
Solve the following pairs of equation
$\frac{2xy}{x+y}=\frac{3}{2},\frac{xy}{2x-y}=\frac{-3}{10},x+y\ne 0,2x-y\ne 0$

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 = 1, y = 7

2. x = -2, y = 2

3. x = 0, y = 8

4. x = 7, y = -8

Q. Solve the equation:
$1.6=\frac{y}{1.5}$

Q. How will you make the following equations linear?
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}+\frac{3}{y-2}=1$
(where $x\ne 1andy\ne 2)$

1. Substitute $x=X+1$ and $y=Y+2$
2. Substitute $\frac{1}{x-1}$ as p and $\frac{1}{y-2}$ as q
3. None of the above
4. The equation is already linear

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.

Is $\sqrt{x}=4$ linear equation? If not then how the equation can be made linear.

1. Yes

2. No, substitute x=u², now the equation is linear in variable x

3. No, substitute x=u², now the equation is linear in variable u

4. None of these

Q. Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite direction they meet in $\frac{9}{7}$ hours. Speed of car starting from point A is:

1. 30 km/hr
2. 90 km/hr
3. 40 km/hr
4. 220 km/hr

Q.

How will you make the following equation linear?

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

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

1. Substitute 1/x-1 as p and 1/y-2 as q

2. substitute x=x+1 and y=y+2

3. The equation is already linear

4. None of the above

Q. $y+3=10$

Q. How the equation $\sqrt{x}=4$ can be made linear? (where $x\ge 0$)

1. Substitute $x=u^2$, now the equation is linear in variable $x$
2. Substitute $x=u^3$, now the equation is linear in variable u
3. Substitute $x=u^2$, now the equation is linear in variable u
4. Substitute $x=u^4$, now the equation is linear in variable u

Q. Solve the following equation:
$\frac{3y+4}{2-6y}=\frac{-2}{5}$

Q. Solve the following pair of equations:
$\frac{1}{x}+\frac{3}{y}=1$
$\frac{6}{x}-\frac{12}{y}=2$
(where $x\ne 0,y\ne 0)$

1. $x=\frac{3}{5},y=\frac{7}{3}$
   
2. $x=\frac{5}{3},y=\frac{15}{2}$
3. $x=4,y=9$
4. $x=3,y=11$

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

Q. Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(where $x>0,y>0)$

1. $x=9,y=4$
2. $x=4,y=9$
3. $x=3,y=2$
4. $x=\frac{1}{2},y=\frac{1}{3}$
   

Q. Solve the following pair of equations:
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}-\frac{3}{y-2}=1$
(where $x\ne 1,y\ne 2)$

1. $x=4$, $y=5$
2. $x=5$, $y=4$
3. $x=\frac{1}{3},y=\frac{1}{3}$
4. None of the above

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