Five years ago, Jacob's age was seven times that of his son. After five years, the age of Jacob will be three times that of his son. Represent this situation algebraically and graphically.

Solve graphically the following pair of equations.
2x-y+3=0 and 3x-5y+1=0

Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

In \(\triangle ABC,\quad \angle C=5\angle B=3(\angle A+\angle B)\),  find all angles of \(\triangle ABC\) .

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

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, then the area is increased by 50 q units. Find the length and the breadth of the rectangle.

Find the value of k, for which system of equations kx+3y=3 and 12x+ky=6 represent parallel lines.

If a motorboat can travel 30 km upstream and 28km down stream in 7 h, it can travel 21 km upstream and return in 5 h. Find the speed of the boat in still water and the speed of the stream.

Given the linear equation 2x+3y-8=0, write another linear equation in two variables such that the geometrical representation of the pair so formed is
(i) intersecting lines.
(ii) Parallel llines.
(ii) coincident lines.

A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 h less than the scheduled time and if the train was slower by 10 km/h, it would have taken 3 h more than the scheduled time. Find the distance covered by the train.

The Resident Welfare Association of a colony decided to build two straight paths in their neighbourhood park such that they do not cross each other, to plant trees along the boundary lines of each path. One of the members of association, Sarika suggested that the paths should be constructed represented by the two linear equations x-3y=2 and -2x+6y=5. Check whether the two paths will cross each other or not. What value is depicted from this action?

A part of monthly charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student X  takes food for 25 days, he has to pay Rs.1750 as hostel charges, whereas a student Y, who takes food for 28 days, pays Rs.1900 as hostel charges. Find the fixed charge and the cost of food per day.

The coach of a cricket team buys 3 bats and 6 balls for Rs.3900 later. He buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.

Draw the graphs of the following equations:
2x - y = 1,x + 2y =13
Find the solution of the equations from the graph and shade the triangular region formed by the lines and the Y-axis.