Solution of Chapter 4. Linear Equation In Two Variables (NCERT Mathematics Exemplar Book)

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 on:

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 Fig. 4.2).

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 times its abscissa.

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

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.

Solve the equation

2x + 1 = x – 3, and represent the solution(s) on

(i) the number line,

(ii) the Cartesian plane.

Find the solution of the linear equation x + 2y = 8 which represent a point on

(i) X-axis (ii) Y-axis

For what value of C, the linear equation 2x + cy = 8 has equal value 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 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 value of x and y are thought to satisfy a linear equation. Write the linear equation-

Draw the graph using the value of x, y as given in the above table.

At what points the graph of the linear equation

(i) cuts the X-axis ?

(ii) cuts the Y-axis?

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

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

(i) if the temperature is 86°F, what is the temperature in Celsius ?

(ii) If the temperature is 35°C, what is the temperature in Fahrenheit ?

(iii) 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?

(iv) What is the numerical value of the temperature which is same in both the scale ?

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.

(i) find the temperature of the liquid in Fahrenheit, if the temperature of the liquid is 313°K.

(ii) If the temperature is 158°F, then find the temperature in Kelvin.

The force exerted to pull a carts 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 ms ^{– 2} (ii) 6 ms ^{– 2}