Linear Equations in Two Variables Maths - Linear Equations in Two Variables

Write whether True or False and justify your answer.
The coordinates of points in the table.

x	0	1	2	3	4
y	2	3	4	-5	6

represent some of the solutions of the equation x – y + 2 = 0.

Write whether True or False and justify your answer.
The graph of every linear equation in two variables need not be a line.

Write whether True or False and justify your answer.

The graph given below represents the linear equation x + y = 0.

Write whether True or False and justify your answer.
The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

Write whether True or False and justify your answer.
The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

Show that the points A(1, 2), B(-1, -16) and C(0, -7) lie on the graph of the linear equation y = 9x - 7.

How many solution(s) of the equation 2x + 1 = x – 3 are there on the:

1. Number line
2. Cartesian plane?

Draw the graph of the equation represented by a straight Line which is parallel to the X-axis and at a distance 3 units below it.

If the point (3, 4) lies on the graph of 3y = ax + 7, then find the value of a.

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is:

1. 5ms^-2
2. 6ms^-2

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation

x	6	-6
y	-2	6

Draw the graph, using the values of x, y as given in the above table. At what points the graph of the linear equation

1. Cuts the X-axis?
2. Cuts the Y- axis?

Draw the graphs of linear equations y = x and y = -x on the same Cartesian plane.
What do you observe?