Friday, May 7, 2010

Problems based on graph

Q1. Draw the graph of 2x+y=6 and 2x-y+2=0. Shade the region bounded by these lines and x-axis. Find the area of the shaded region.
Q2. Solve the following equations graphically: 2x+3y=12; x-y=1
(i) Shade the region between the two lines and x-axis.
(ii) Shade the area bounded by these lines and the y-axis.
(iii) Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis.
Q3. Solve the following system of linear equations graphically x-y=1; 2x+y=8 Shade the area bounded by these two lines and the y-axis.
Q4. Solve the following system of linear equations graphically: 2x-3y=1; 3x-4y=1. Does the point (3,2) lies on any of the line?
Q.5 Solve the following system of linear equations graphically: 4x – 5y – 20 =0 ;
3x + 5y –15 = 0 Determine the vertices of the triangle formed by the lines, representing the above equations, and the y-axis.
Q6. Draw the graphs of the equations 2x + y =6 and 2x – y + 2 =0.
a)Determine the vertices of the triangle formed by the lines, representing the above equations, and the x-axis.
b)Shade the region bounded by these lines and x-axis.
c)Find the area of the shaded region.
Q7.Solve graphically the system of linear equations 5x – 6y + 30 = 0,
5x + 4y – 20 = 0. Find the area of the regions bounded by these lines and the x-axis.
Q8.Draw the graphs of the equations: 3x + y – 11 = 0, x – y – 1 = 0 .Find the vertices of triangle formed by the above two lines and x = 0.
Q9. Draw the graphs of the following equations: 4x+3y=24 2x-y-2=0
(i) Find the coordinates of the points where the lines meet the x-axis.
(ii) Find the area of the region bounded by these lines and x-axis.
(iii) Find the area of the region bounded by these lines and y-axis.
Q10. Observe the graph representing pair of linear equations in two variables.
x+y=3 and x-3y=6 given below and answer the following questions:

1)Find the coordinates of the point where line meets x-axis and y-axis.
2)Shade the region bounded by above lines and y-axis
3) Find the vertices of triangle formed by the above two lines and x = 0.
4) Find the area of the region bounded by these lines and y-axis