This document provides 12 problems involving linear equations in two variables. The problems cover finding values that satisfy equations, expressing variables in terms of others, determining if points lie on lines, drawing graphs of equations, finding equations of lines passing through points, and word problems involving rates and distances. The full range of skills for solving and applying linear equations in two variables is represented.

1. ASSINGNMENT CLASS IX
LINEAR EQUATION IN TWO VARIABLES
1. Find the value of k in the equation 2x+y=k if x=3 and y=5.
2. Express x in the terms of given that x/3+2y=5. Check whether
(3, 2) is a solution of the given equation.
3. For what value of p the point (p, 4) lies on the line 3x+y=10?
4. Give the geometric representation of 2x+7=0:-
I. In one variable.
II. In two variables.
5. Write two solutions of the equation 5x+4y=0.
6. Draw the graph of 2x+y=8.
7. If the point (3, 4) lie on the graph of equation 3y=ax+7, find the
value of ‘a’.
8. By drawing the graph of 3x-2y=4 and x+y-3=0, find the value of x
and y.
9. Give the equation of two lines passing through (3, 4). How many
more such lines are there and why?
10. Find the cost of a car if selling price of car is Rs. 72000 and
profit 20%
11. The perimeter of a rectangular plot is 120m. If the length of
the plot is decreased by 5m and breadth is increased by5m, the
area is increased by 75sqm. Find the length and the breadth of
the rectangular plot.
12. If a driver drives at a speed of 24km/hr, he reaches his
destinations 5minutes too late. But if he drives at the speed of
30km/hr, he reaches his destination 4 minutes soon. How far is
his distance?