Pair of Linear ...

When a bucket is half full, the weight of the bucket and the water is $10\text{ kg}$. When the bucket is two-thirds full, the total weight is $11\text{ kg}$. What is the total weight, in kg, when the bucket is completely full?

If $2x + 3y = 24$ and $2x - 3y = 12$, then the value of $xy$ is ___________.

Choose the correct answer from the alternatives given.
If $\displaystyle \frac{x \, + \, y \, - \, 8}{2} \, = \, \frac{x \, + \, 2y \, - \, 14}{3} \, = \, \frac{3x \, + \, y \, - \, 12}{11}$ then find the values of x and y, respectively. 

$ax + 2y = 5$
$3x - 6y = 20$
In the system of equations above, $a$ is a constant. if the system has one solution, which of the following CANNOT be the value of $a$?

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically and find their present ages.

$\dfrac{22}{x+y}+\dfrac{15}{x-y}=5$
$\dfrac{55}{x+y}+\dfrac{45}{x-y}=14$

Find the solution of pair of equations $\dfrac{x}{10}+\dfrac{y}{5}-1=0$ and $\dfrac{x}{8}+\dfrac{y}{6}=15.$ Hence, find $\lambda$, if $y=\lambda x+5$.

Solve by using substitution method. $3x +4y =10$ & $2x - 2y =2$

Solve the following pair of equations graphically; $2x -3y =1,$ & $4x -3y +1=0$

Solve each pair of equation by using the substitution method.
$x+\dfrac{6}{y}=6$
$3x-\dfrac{8}{y}=5$