Worksheet solutions for chapter: Linear Equations in Two Variables for class 9 are provided below.
(1)Express the following linear equations in the form ax + by +c = 0 and indicate the values of a, b and c in each case:
(i) 3x + 5y = 3 (ii) 2x + 4 = 0
(i) 3x + 5y = 3 can be written as 3x + 5y – 3 = 0. Here, a = 3, b = 5 and c = -3.
Hence, a = 3, b = 5 and c = -3.
(ii) 2x + 4 = 0
2x + 4 = 0 can be written as 2x + 0.y + 0 = 0.Here, a = -2, b = 3 and c = -6.
Hence, a = 2, b = 0 and c = 0.
(2)Write two solutions for the equation 3x + 6y = 9.
(3)Find the value of k, if x = 3 and y = 1 is a solution of the equation 6x + y = k.
Put x = 3 and y = 1 in equation 6x + y = k
6(3) + 1 = k
18 + 1 = k
19 = k
k = 19
Hence, value of k is 19.
(4)Draw the graph of equation 4x = y.
4x = y
4x – y = 0
Solutions of the equation
Put x = 0
4(0) – y = 0
y = 0
Therefore (0, 0) is a solution of given equation.
Put y = 2
4x – 2 = 2
4x = 4
x = 1
Therefore (1, 2) is a solution of given equation.
Hence, (0, 0) and (1, 2) are the two solutions of the given equation.
Solutions of the equations are tabulated below to draw a graph-
AB is required linear equation in two variables.
(5) Give the equations of two lines passing through (1,7). How many more such lines are there and why?
The solutions of equations are (1, 7).
Equations which satisfy these solutions are
x + y = 8
7x = y
These are some equations which can satisfy given solutions. There can be infinite lines or equations which will satisfy the given solutions or coordinates.
(6) If the distance covered by a car is directly proportional to speed of the car. Express this in the form of an equation in two variables and draw a graph by taking constant time as 4 units.
(7) If the point (2, 6) lies on the graph of the equation x + by = 14, find the value of b.
Point (2, 6) lies on the graph of equation x + by = 14.
Therefore, x = 2 and y = 6
Put these values in equation x + by = 14
2 + b (6) = 14
6b = 14 – 2
6b = 12
b = 2
Hence, the value of b is 2.
(8) Write each of the following as an equation in two variables:
(i) x = 5 (ii) 2y = 5
(i) x = 5 can be written as x + 0.y -5 = 0.
(ii) 2y = 5 can be written as 0.x + 2y -5 + 0.
Choose the correct answer-
(9)A linear equation in two variables has
(i) only one solution
(ii) infinitely many solutions
(10) The graph of x = a is a straight line parallel to
(i) x – axis
(ii) y- axis