NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 1(iv)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 1(iv)

Question:

Solve the following pair of linear equations by the substitution method: 0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3

Given:

The given equations are:

0.2x + 0.3y = 1.3 ---(1)

0.4x + 0.5y = 2.3 ---(2)

To Find:

We need to find the values of x and y that satisfy both equations.

Formula:

Substitution method: Solve one equation for one variable and substitute it into the other equation.

Solution:

From equation (1), we can express x in terms of y:

0.2x = 1.3 - 0.3y ⇒ x = 1.3 - 0.3y0.2

Substitute this value of x into equation (2):

0.4(1.3 - 0.3y0.2) + 0.5y = 2.3

Simplify and solve for y:

2(1.3 - 0.3y) + 0.5y = 2.3 ⇒ 2.6 - 0.6y + 0.5y = 2.3 ⇒ -0.1y = -0.3 ⇒ y = 3

Substitute y = 3 back into the expression for x:

x = 1.3 - 0.3(3)0.2 = 1.3 - 0.90.2 = 0.40.2 = 2

Result:

Therefore, the solution to the pair of linear equations is x = 2 and y = 3.

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