NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1
Question 9

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 (\(10x - 14y = -4\)).

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 3: Pair of Linear Equations in Two Variables – Exercise 3.1 | Detailed Answers