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

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

Question:

Solve the following pair of linear equations by the substitution method.
3x 2 - 5y 3 = -2
x 3 + y 2 = 13 6

Given:

The given pair of linear equations are:
3x 2 - 5y 3 = -2 ...(1)
x 3 + y 2 = 13 6 ...(2)

To Find:

We need to solve the given pair of linear equations by the substitution method.

Formula:

Substitution method involves solving one equation for one variable and substituting it into the other equation.

Solution:

From equation (2):
x 3 + y 2 = 13 6
⇒ x + 3y 2 = 13 2
⇒ 2x + 3y = 13 ...(3)
From equation (1):
3x 2 - 5y 3 = -2
⇒ 9x - 10y = -12 ...(4)
From (3), x = 13-3y 2
Substitute this value of x in (4):
9( 13-3y 2 ) - 10y = -12
⇒ 9(13 - 3y) - 20y = -24
⇒ 117 - 27y - 20y = -24
⇒ 117 - 47y = -24
⇒ 47y = 141
⇒ y = 3
Substitute y = 3 in (3):
2x + 3(3) = 13
⇒ 2x + 9 = 13
⇒ 2x = 4
⇒ x = 2

Result:

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