Class 10th-Linear Equations in Two Variables -2

Class-X

Pair of Linear Equations in Two Variables

1.       Form the pair of linear equations in the following problems, and find their solutions graphically.

          i) 10 students of Class X took part in a Mathematics quiz. 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.

          ii) 5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens         together, whereas 7 pencils and 5 pens together cost Rs.46. Find the cost of           pencil  and that of one pen.

2.       Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically.

          i) x+y=5,2x +2y=10

          ii) x-y=8, 3x-3y=16

          iii) 2x+y-6=0, 4x-2y-4=0

          iv)2x-2y-2=0,4x-4y-5=0

3.       Half the perimeter of a rectangular garden, whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.

4.       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 lines

          iii) coincident lines

5.       Draw the graphs of the equations x-y+1=0 and 3x+2y-12=0.Determine the coordinates of the vertices of the triangle formed by these lines and the x- axis and the shade the triangular region.

6.       Draw the graphs of equations:

          3x-y=3

          x-2y=-4

Shade the area of region bounded by the lines and x- axis.

7.       In a bag, there are 175 notes and Rs.5 and Rs.10 denominations. If their total value is 1000.Solve it graphically and find number of each type of note.

8.       Solve it graphically:

The age  of Sanjay is 4 times the age of his son. 5 years hence the age of Sanjay will be three times the age of his son. Find their present ages.

9.       Draw the graphs of linear equations

          x-y=-1

          and 3x+2y=12.

Calculate the area bounded by these lines and x-axis.

10.     Solve it  graphically:

There are two examination rooms A and B. If 10 candidates are sent  from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

Compiled by:-

Sanjeev Kumar Taneja

Mathematics District Resource Person(Ludhiana)