Pair of Linear ...

Using graphical method check whether the given equation is consistent:

The equations $$4x - y = 1$$ and $$2x - 2y = 2$$ are __________.

The equation $$-4x - 4y = 2$$ and $$-2x - 2y = 1$$ have _________.

The sum of unit place and tens place digits of a two digit number is $$12$$. If the new number formed by reversing those digits is less than the original number by $$18$$. Find the original number.

Some students are divided into two groups A & B. If $$10$$ students are sent from A to B, the number in each is the same. But if $$20$$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.

If the sum of $$2$$ real numbers is $$20$$ and their difference is $$6$$, find the value of their product.

If $$2a = b$$, the pair of equations $$x + 2y = 2a - 6b, ax + by = 2a^{2} - 3b^{2}$$ possess _____ solution(s)

If the system of linear equations  $$\displaystyle\begin{cases}\dfrac12x - \dfrac23y = 7\\ax-8y = -1\end{cases}$$ has no solution then the value of constant $$a$$ is.

Henry is three times as old as Truman. Two years ago, Henry was five times as old as Truman. How old is Henry now?

If $$\left| x \right| +x+y=10$$ and $$x+\left| y \right| -y=12$$ then find the value of '$$x+y$$'.