NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 1(iv)
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 1(iv)
Question:
Solve the following pair of linear equations by the elimination method and the substitution method: x2 + 2y3 = -1 and x - y3 = 3
Given:
The given pair of linear equations are:x2 + 2y3 = -1 ---(1)
x - y3 = 3 ---(2)
To Find:
We need to solve the given pair of linear equations using the elimination method and the substitution method.Formula:
No specific formula, we will use the elimination and substitution methods.Solution:
Elimination Method:
Multiply equation (2) by 2: 2x - 2y3 = 6 ---(3)
Add equations (1) and (3): x2 + 2x + 2y3 - 2y3 = -1 + 6 ⇒ 5x2 = 5 ⇒ x = 2 Substitute x = 2 in equation (2): 2 - y3 = 3 ⇒ y = -3
Multiply equation (2) by 2: 2x - 2y3 = 6 ---(3)
Add equations (1) and (3): x2 + 2x + 2y3 - 2y3 = -1 + 6 ⇒ 5x2 = 5 ⇒ x = 2 Substitute x = 2 in equation (2): 2 - y3 = 3 ⇒ y = -3
Substitution Method:
From equation (2), x = 3 + y3 ---(4)
Substitute (4) in equation (1): 3 + y/32 + 2y3 = -1
⇒ 9 + y6 + 4y6 = -1 ⇒ 9 + 5y = -6 ⇒ 5y = -15 ⇒ y = -3
Substitute y = -3 in equation (4): x = 3 + -33 = 3 - 1 = 2
From equation (2), x = 3 + y3 ---(4)
Substitute (4) in equation (1): 3 + y/32 + 2y3 = -1
⇒ 9 + y6 + 4y6 = -1 ⇒ 9 + 5y = -6 ⇒ 5y = -15 ⇒ y = -3
Substitute y = -3 in equation (4): x = 3 + -33 = 3 - 1 = 2
Result:
The solution of the given pair of linear equations is x = 2 and y = -3.Next question solution:
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(i)Explore more in Pair of Linear Equation:
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