## MP Board Class 9th Maths Solutions Chapter 4 Linear Equations in Two Variables Ex 4.1

Question 1.

The cost of notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

Solution:

Let cost of pen be ₹ x and cost of a notebook be ₹ y

y = 2x

y – 2x = 0.

Question 2.

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

- 2x + 3y = 9.3\(\overline { 5 } \)
- x – \(\frac{y}{5}\) – 10 = 0
- -2x + 3y = 6
- x = 3y
- 2x = – 5y
- 3x + 2 = 0
- y – 2 = 0
- 5 = 2x

Solution:

1. 2x + 3y = 9.3\(\overline { 5 } \)

2x + 3y – 9.3\(\overline { 5 } \) = 0

a = 2, b = 3, c = – 9.3\(\overline { 5 } \)

2. x – \(\frac{y}{5}\) – 10 = 0

a = 1, b = – \(\frac{1}{5}\), c = – 10

3. -2x + 3y = 6

– 2x + 3y – 6 = 0

a = – 2, b = 3, c = – 6

4. x = 3y

1. x – 3y + 0 = 0

a – 1, b = – 3, c = 0

5. 2x = – 5y

2x + 5y + 0 = 0

a = 2, b = 5, c = 0

6. 3x + 2 = 0

3x + 0y + 2 = 0

a = 3, b = 0, c = 2

7. y – 2 = 0

0x + y – 2 = 0

a = 0, b = 1, c = – 2

8. 5 = 2x

– 2x + 0y + 5 = 0

a = – 2, b = 0, c = 5

Solution of a Linear Equation:

Consider a Linear equation x + 2y = 6

Let x = 2 and y = 2.

Then L.H.S. of the equation = x + 2y = 2 + 2 x 2 = 6

and R.H.S. of the equation = 6 (given)

i.e., LHS. = R.H.S. for x = 2 and y = 2.

Therefore, x = 2 and y = 2 i.e., (2, 2) is the solution of the given equation x + 2y = 6.

Any pair of values of x and y which satisfies the given equation is called a solution of the equation. A linear equation in two variables has infinitely many solutions.

Note:

To find the solution of an equation, assure a value of one of the variable and calculate the value of second variable from the given equation.