Linear equations in two variables class 9 questions are provided here for students to understand the concept very well as well as to get good grades in the final examinations. As a complete explanation is given for each question, students can find these questions useful to score good marks. Linear equations in two variables class 9 questions are framed as per the CBSE and NCERT curriculum. We have also provided practice problems for the students so that students can improve their problem-solving capabilities. To learn more about linear equations in two variables class 9, click here.

Linear Equations in Two Variables Class 9:

In Linear equations in two variables class 9, students can learn different concepts such as introduction to a linear equation in one variable, a linear equation in two variables, process of finding the solution to the given linear equations, graphing methods and so on.

Also, read: Linear Equations.

Linear Equations in Two variables Class 9 Questions with Solutions

Linear Equation in Two Variables Definition:

An equation is said to be a linear equation in two variables if it has two variables with degree one. The standard form for linear equation two variables is given by:

Ax + By + C = 0,

Where

A, B and C are real numbers. Also, A and B should not be equal to 0.

x and y are variables.

Also, read: Linear Equation in One Variable.

1. Write the linear equation 3x = -7y in the form Ax + By + C = 0 and determine the value of A, B and C.

Solution:

Given equation: 3x = -7y

As we know, the standard form of linear equation in two variables is Ax + By + C = 0

Thus, the given equation is written as:

3x + 7y + 0 = 0

Now, compare the above equation with the standard form, we get

A = 3, B = 7 and C = 0.

2. Determine the value of p, if (2, 0) is the solution of the linear equation 2x + 3y = p.

Solution:

Given linear equation: 2x + 3y = p

Now, substitute x = 2 and y = 0 in the given linear equation, we get

2(2) + 3(0) = p

4 + 0 = p

p = 4.

Therefore, the value of p is 4.

3. Give three solutions for the linear equation x = 4y.

Solution:

To determine three solutions for the linear equation x = 4y, substitute different values for the variables x and y.

If x = 0, then 0 = 4y

⇒ y = 0

If x = 1, then 1 = 4y

⇒ y = ¼

If x = 2, then 2 = 4y

⇒ y = 2/4 = 1/2

Therefore, we get

x

0

1

2

y

0

1/4

1/2

Therefore, the three solutions for x = 4y are (0, 0), (1, ¼) and (1, ½).

4. The cost of a pen is Rs. 5 less than half the cost of the notebook. Express the given statement in the form of a linear equation in two variables.

Solution:

Let the cost of the pen be x and the cost of the notebook be y.

According to the given condition, we can write

x = (½)y – 5

Now, the above equation can be written as:

x = (y/2) – 5

2x = y – 10

Rearranging the obtained equation, we get

2x – y + 10 = 0, which is the required linear equation in two variables.

5. Determine the point “P” if the graph of linear equation 2x + 3y = 6 cuts the Y-axis.

Solution:

Given linear equations: 2x + 3y = 6

As we know, if the graph of the linear equation cuts the y-axis, then the x – coordinate should be 0.

Thus, substituting x = 0 in the given linear equation,we get

2(0) + 3(y) = 6

0 + 3y = 6

3y = 6

y = 6/3

y = 2

Therefore, the point P = (0, 2)

Hence, the graph of linear equation 2x + 3y = 6 cuts the Y-axis at the point (0, 2).

6. Is (0, 2) is the solution of a linear equation x – 2y = 4.

Solution:

Given linear equation: x – 2y = 4

Now, substitute x = 0 and y = 2 in the given equation.

⇒ 0 – 2(2) = 4

⇒ – 4 ≠ 4

Therefore, (0, 2) is not a solution of a linear equation x – 2y = 4.

7. Write the equation 5x = 7/2 in the form of a linear equation in two variables.

Solution:

The equation 5x = 7/2 in the linear equation in two variables is:

5x + 0y – (7/2) = 0

The above obtained equation can also be written as:

10x + 0y – 7 = 0

8. Determine the solution for the linear equation.

Solution:

The linear equation 2x – 5y = 7 has infinitely many solutions.

Explanation:

Given equation: 2x – 5y = 7.

Thus, the equation can be written as follows:

-5y = 7 – 2x

y = -(7-2x) / 5

So, we get different “y” values if we use different “x” values.

Hence, we can conclude that the linear equation 2x – 5y = 7 has infinitely many solutions.

9. How to express the equation x = 9 in the form of a linear equation in two variables?

Solution:

Given equation: x = 9

It can also be written as x – 9 = 0

The standard form of linear equation in two variables is Ax + By + C = 0

Now, comparing the given equation and the standard form, we get

A = 1, B = 0 and C = -9.

Thus, the equation x = 9 in the form of linear equation in two variables is written as:

1x + 0y – 9 = 0

10. Draw the linear equation graph, given that the solutions are represented using the points in which the sum of the coordinates equals 10

Solution:

According to the given condition, we can write:

x + y = 10

Hence, y = 10 – x.

Now, let us randomly assume few values:

If x = 0, then y = 10 – 0 = 10

⇒ (0, 10)

If x = 5. Then y = 10 – 5 = 5

⇒ (5, 5)

If x = 10, then y = 10 – 10 = 0

⇒ (10, 0)

Now, plot the values (0, 10), (5, 5) and (10, 0) in the graph, we get the graph of the linear equation x + y = 10.

Linear equations in two variables class 9 questions

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Practice Questions

Answer the following:

  1. Check whether the given statement is true or false: (0, 3) is the solution of the linear equation 3x + 4y = 12.
  2. Prove that the points P(1, 2), Q(-1, -16), R(0, -7) lie on the graph of equation y = 9x – 7.
  3. Identify four solutions of the linear equation: x + πy = 4.

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