Grade 10 : Pair of Linear equations in 2 variables @1

3. Pair of Linear equations in two variables

Grade : 10

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1. Solve the following systems of equations graphically:

a) 2x - 3y +13 =0, 3x - 2y +12 = 0

b) 2x + 3y +5 = 0, 3x - 2y -12 =0

c) x+y =4, 2x - 3y =3

d) 3x + 2y =12, 5x -2y =4

e) x + 2y - 7 = 0,  2x - y - 4 = 0

2. Determine graphically whether the system of equations x -2y = 2, 4x - 2y =5 is consistent or in-consistent.

3. Draw the graphs of the following equations on the same graph paper:

    2x +3y =12, x - y = 1.

   Find the coordinates of the vertices of the triangle formed by the two straight lines and the y axis.

4. Draw the graphs of x - y +1 =0 and 3x + 2y -12 =0 . Determine the coordinates of the vertices of the triangle formed by these lines and x axis and shade the triangular area. Calculate the area bounded by these lines and x axis.

5. Solve the system of equations graphically and shade the region between the lines and the y axis.
   3x - 4y =7, 5x + 2y =3

6. Represent the pair of equations graphically and write the coordinates of the points where the lines intersects y axis .
x + 3y =6, 2x - 3y =12

7. Draw the graph of the equations x=3, x=5, 2x - y- 4 =0, Also, find the area of the quadrilateral formed by the lines and the x axis.

8. Solve the system of equations graphically .
    2x + y =6, 2x -y +2 =0.
   Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x axis and the lines with the y axis.

ANSWERS