NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1Question 9
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1
Question. 9
9. One equation of a pair of dependent linear equations is \(-5x + 7y = 2\). The second equation can be
(A)
\(10x + 14y + 4 = 0\)
(B)
\(-10x - 14y + 4 = 0\)
(C)
\(-10x + 14y + 4 = 0\)
(D)
\(10x - 14y = -4\)
Detailed Answer with Explanation:
Step 1: Recall condition for dependent equations.
If two linear equations are dependent, one is just a multiple of the other. That means all their coefficients are in the same ratio.
Step 2: Start with the given equation.
Equation: \(-5x + 7y = 2\).
Step 3: Multiply to create an equivalent equation.
If we multiply the entire equation by \(-2\):
\((-2)\times(-5x) + (-2)\times(7y) = (-2)\times 2\)
\(10x - 14y = -4\)
Step 4: Compare with the options.
This matches exactly with Option D.
Final Answer: Option D (\(10x - 14y = -4\)).