WORKSHEET GRADE 10 LINEAR EQUATIONS IN TWO VARIABLES

 SET - 1

1. On comparing the ratios , without drawing them find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide:

 (i) 5x – 4y + 8 = 0 & 7x + 6y = 0     (ii) 9x +3y + 12 = 0 & 18x + 6y+ 24 = 0 

(iii) 6x – 3y + 10= 0 & 2x –y + 9 =0

2. Solve the following system of equations graphically: 3x + 2y – 11 = 0 and 2x – 3y + 10 = 0

3. Draw the graphs of x – y +1 = 0 and 3x +2y – 12 = 0. Calculate the area bounded by these lines and the x axis.

4. Solve the following system of equations graphically: x +2y = 1 and x -2y = -7. Also read the points from the graph where the lines meet the axis of x.

5. Draw the graph of x + 2y – 7 = 0 and 2x – y – 4 = 0. Shade the area bounded by these lines and y axis.

6. Draw the graphs of the following system of linear equations on the same graph paper 2x – y = 1,

 x +2y = 13.

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

7. Draw the graphs 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.

8. Solve graphically solve 2x – 3y + 13 = 0 and 3x – 2y – 12 = 0

SET - 2

1. Solve the following system of equations using method of substitution:

    (i) x + y = 14 , x – y = 4      (ii) 4x – 8y = -4 , 7x – 14y = -7

    (iii) x +2y = 3 and 2x + 4y = 8     (iv) 7(y+3) -2(x+2) =14 and 4(y-2) + 3(x -3) = 2

2. Solve the each of the following systems of equations by using the elimination  method 

  (i) x + y = 7 and 5x +12y = 7         (ii) 2x + 3y = 17 and 3x – 2y = 6

  (iii) 2x – y – 3 = 0 and 4x + y – 3 = 0        (iv) 2x +y -35 = 0 and 3x +4y – 65 = 0

  (v) x + 2y + 1 = 0 and 2x – 3y – 12 = 0     (vi) 2x – y = 6 and x –y = 2

 3. Solve ax + by = a-b and bx – ay = a+b

4. Solve the following system of equations in x and y

   (a-b) x + (a+b)y = a²-2ab + b²  and (a+b) (x+y) = a² + b ²

5. For each of the following system of equations determine the values of k for which the given system has no solutions

 (i) 3x – 4y + 7 = 0 and kx + 3y – 5 = 0    (ii) 2x – ky + 3= 0 and 3x +2y -1 =0

 (iii)  3x + y = 1 and (2k-1)x + (k-1)y = 2k +1   (iv) kx – 5 y = 2 and 6x +2y = 7 

  (v) 2x +ky = 11 and 5x – 7y = 5