Linear Equations

Step 1: Condition for infinitely many solutions.
For the system of equations to have infinitely many solutions, the two equations must be dependent. This happens when the ratios of the coefficients of , , and the constants are equal. For the system:
Step 2: Solving for .
From the first and third ratios: Now, solve the middle ratio: Thus, the system has infinitely many solutions when . The correct answer is (4) 6 or 8.