NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 1(iii)
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 1(iii)
Question:
Solve the following pair of linear equations by the substitution method:
3x – y = 3
9x – 3y = 9
Given:
The given pair of linear equations is:
3x – y = 3 ---(1)
9x – 3y = 9 ---(2)
To Find:
We need to find the values of x and y that satisfy both equations using the substitution method.
Formula:
Substitution method involves solving one equation for one variable and substituting it into the other equation.
Solution:
From equation (1), we can express y in terms of x:
y = 3x – 3
Substitute this expression for y into equation (2):
9x – 3(3x – 3) = 9
Simplify and solve for x:
9x – 9x + 9 = 9
9 = 9
This equation is always true, indicating that the two equations are linearly dependent (represent the same line).
Therefore, there are infinitely many solutions. Any point (x, y) that satisfies equation (1) also satisfies equation (2).
Result:
The given equations are linearly dependent, and there are infinitely many solutions.
Comments
Post a Comment