Question

The pair of equations \(x + y = 5\) and \(2x + 2y = k\) has infinitely many solutions if \(k =\)

• A. 4
• B. 6
• C. 8
• D. 10

Hint:

When two linear equations are multiples of each other, they represent the same line and thus have infinitely many solutions.

Answer 1

The Correct Option is D

For the pair of equations to have infinitely many solutions, the second equation must be a multiple of the first equation. The first equation is \(x + y = 5\), and the second equation is \(2x + 2y = k\). Multiplying the first equation by 2, we get \(2x + 2y = 10\), so for infinitely many solutions, \(k = 10\). Thus, the correct answer is option (4).