NCERT Exemplar solutions for Mathematics [English] Class 9 chapter 4 - Linear Equation In Two Variables [Latest edition]

The linear equation 2x – 5y = 7 has ______.

The equation 2x + 5y = 7 has a unique solution, if x, y are ______.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is ______.

Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form ______.

The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point ______.

The equation x = 7, in two variables, can be written as ______.

Any point on the x-axis is of the form ______.

Any point on the line y = x is of the form ______.

The equation of x-axis is of the form ______.

The graph of y = 6 is a line ______.

x = 5, y = 2 is a solution of the linear equation ______.

If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form ______.

The positive solutions of the equation ax + by + c = 0 always lie in the ______.

The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point ______.

The graph of the linear equation y = x passes through the point ______.

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation ______.

How many linear equations in x and y can be satisfied by x = 1 and y = 2?

The point of the form (a, a) always lies ______.

The point of the form (a, – a) always lies on the line ______.

The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.

The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

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

The graph given below represents the linear equation x = 3 (see figure).

The coordinates of points in the table:

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

Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

The graph of every linear equation in two variables need not be a line.

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

Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is `1 1/2` times its abscissa.

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.

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.

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

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

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

Find the solution of the linear equation x + 2y = 8 which represents a point on x-axis.

Find the solution of the linear equation x + 2y = 8 which represents a point on y-axis.

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.

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.

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

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 graph of the linear equation 3x + 4y = 6. At what points, the graph cuts the x-axis and the y-axis.

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation

`C = (5F - 160)/9`

1. If the temperature is 86°F, what is the temperature in Celsius? 
2. If the temperature is 35°C, what is the temperature in Fahrenheit?
3. If the temperature is 0°C what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
4. What is the numerical value of the temperature which is same in both the scales?

If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation

`y = 9/5 (x - 273) + 32`

1. Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.
2. If the temperature is 158°F, then find the temperature in Kelvin.

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 (i) 5 m/sec², (ii) 6 m/sec².