Linear Equations In Two Variables – Class 9/ Maths.

Chapter 4 of NCERT/CBSE class 9 Maths is about Linear equations in two variables. Here in this lesson you can find practice problems for this chapter.

CBSE CLASS 9 MATHEMATICS
Linear Equations In Two Variables – Chapter 4 / Sample Papers.
Answer the following questions:

1. If the point (3, 4) lies on the line 2y = ax + 8, then find the value of a?
   Solution:
   Since the point (3, 4) lies on the line 2y = ax +8, we can write 2 x 4 = a x 3 + 8.
   8 = 3a + 8
   3a = 8 – 8 = 0
   Therefore, a = 0
2. Find two solutions for the equation 3x – 2y = 6.
   Solution:
   Taking x = 0, we get -2y = 6
   That is, y = 6/ (-2) = -3.
   So (0, -3) is a solution of the given equation.
   Similarly, by taking y = 0, we get 3x = 6
   That is x = 6/3 = 2.
   So (2, 0) is a solution of the given equation.
3. Show that the points (0, 7), (1, 5), (2, 3) and (4, -1) lie on the graph of the linear equation 2x + y = 7.
   Solution:
   Given equation is 2x + y = 7
   At (0, 7); LHS = 2 x 0 + 7 = 0 + 7 = 7 = RHS.
   At (1, 5); LHS = 2 x 1 + 5 = 2 + 5 = 7 = RHS.
   At (2, 3); LHS = 2 x 2 + 3 = 4 + 3 = 7 = RHS.
   At (4, -1); LHS = 2 x 4 + (-1) = 8 + (-1) = 7 = RHS.
4. Find the value of k, if x = 3, y = 4 is a solution of the equation 3x – y = k.
   Solution:
   Given 3x – y = k
   Put x = 3 and y = 4 in the given equation 3x – y = k
   3 x 3 – 4 = k
   9 – 4 = k
   5 = k.
   So the value of k is 5.
5. Determine the point on the graph of the linear equation 2x + 3y = 8, whose ordinate is 2 times its abscissa.
   Solution:
   Given ordinate is 2 times its abscissa, which means that y = 2x.
   Put y = 2x in the given equation 2x + 3y = 8, we get 2x + 3(2x) = 8.
   2x + 6x = 8
   8x = 8
   x = 8/8 = 1.
6. Solve the equation 2x + 1 = x – 3.
   Solution:
   2x + 1 = x -3
   2x – x = -3 -1
   x = -4
7. Find the co-ordinates of points where the graph of the equation x + 2y = 8 intersects x axis and y axis.
   Solution:
   Given equation is x + 2y = 8.
   For intersection with x axis, y = 0.
   Therefore, x = 8.
   So the coordinates are (8, 0).
   For intersection with y axis, x = 0.
   2y = 8
   y = 8/2 = 4
   So the coordinates are (0, 4).