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.
$$x+\dfrac{6}{y}=6$$
$$3x-\dfrac{8}{y}=5$$