Draw the graphs of the pair of linear equations $x+y=10$ and $x-y=4$. Determine the coordinates of the vertices of the triangle formed by these linear equations and the $X$-axis.

Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

If in a rectangle,the length is increased and breadth reduced each by $2$ units,the area is reduced by $28$ square units. If,however,the length is reduced by $1$ unit and the breadth increased by $2$ units,the area increases by $33$ square units. Find the area of the rectangle.

Graphically,solve the following pair of equations:
$2x + y = 6$
$2x - y + 2 = 0$
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the $x$-axis and the lines with the $y$-axis.

Solve the following pairs of equations:
$43x + 67y = -24$
$67x + 43y = 24$