Eqns. Reducible to Pair of LE in 2 Variables

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. $x=3,y=11$

4. $x=4,y=9$

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.

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

2. 2, 3

3. 3, 2

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

Q.

Separate the variables in the below given equation.

7x - 2y = 5xy

After separating the variables equation is of the form

$\frac{7}{\square }$ - $\frac{2}{\square }$ = 5

1. y, x, 0, 1

2. y, x, 1, 1

3. x, y, 0, 1

4. x, y, 1, 0

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. None of the above

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

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

4. The equation is already linear