Linear Equation In Two Variables
Topic Covered : Graph and Condition for Solvability of L.E.
Q1 :- Draw the Graphs of the given equations ; 2x – 3y + 6 = 0 ; 2x + 3y – 18 = 0 ;
y -2 = 0 Find the vertices of the triangle so obtained. Also find the area of the triangle
Q2 :- Solve the following system of linear equations graphically
4x – 5y - 20 = 0 ; 3x + 5y - 15 = 0 , Determine the vertices of triangle formed by
lines representing the equations and the Y – axis .
Q3:- Solve 5x – y = 7 ; x – y + 1 = 0 ,graphically & calculate the area bounded by these
lines and the Y – axis.
Q4:- For what value of k , will the following system of equations have infinite solution
2x + 3y = 4 ; ( k + 2) x + 6y = 3k + 2
Q5 :- Find the value of p and q for which the following system of equations has infinite
number of solution
2 x + 3 y = 7 ; ( p + q ) x + ( 2 p – q ) y = 21 .
Q6 :- Determine the value of k so that following linear equation have no solution ;( 3 k + 1 ) x + 3y - 2 = 0 ; ( k2 + 1 ) x + ( k – 2 ) y - 5 = 0
Q7 :- For what value of a and b for which the given equation has infinite solution
2x – 3y = 7 ; ( a + b ) x - ( a + b – 3 ) y = 4a + b
Q8 :- Obtain the condition for the following system of linear equation to have a unique
solution ax + by = c ; lx + my = n
Q9 :- Prove that there is a value of c ( ≠ 0 ) for which the system 6x + 3y = c – 3 ;
12x + cy = c has infinite solution , find this value of c .
Q10 For what value of k for which the following system of equation have unique solution:6x + 5y = 11 ; 3x + 4y = k
Q11:- Show graphically that x =3 , y = 2 is not a solution of the system of equations
3x – 2y = 5 ; 2x + y = 7
Q12 :- Show graphically that the system of linear equations 2x – 3y = 5 , 6y – 4x = 3 is
inconsistent .
Q13:- Draw the graph of the following equations on the graph 2x + y = 2 ; 2x + y = 6 , find
the coordinates of the vertices of the trapezium formed by these lines .Also , find the area of
the trapezium so formed .
Q14 :- Use a single graph paper and draw the graph of the following equations :
2y – x = 8 ; 5y – x = 14 , y – 2x = 1 .Obtain the vertices of the triangle so obtained.
Q15 :- 10 students of a class took part in quiz competition . If the number of girls is 4 more
than the number of boys . Find the number of boys and girls who took part in the quiz.
Question
Answer
Question
Answer
1
( 3, 4 )
(0 , 2 )
(6,2)
; 6 sq. unit
Answer
2
3
( 0, - 4 ), 8 sq
(0,3)
unit
(5,0)
13
( 0, 2) , ( 1 , 0 ) ,
( 3, 0 ) , ( 0 , 6 ) ;
8 sq. unit
14
( - 4 , 2 ),
(1,3),
(2,5)
4
5
6
7
8
2
15
-1
a = -5
b = -1
am ≠ bl
15
Girls = 7
Boys = 3
9
10
Any
6 Real
Number