Linear Equations

Step 1: Condition for infinite solutions.
For a system of linear equations to have an infinite number of solutions, the two equations must be dependent, i.e., they must be multiples of each other.

Step 2: Comparing the two equations.
We compare the two equations: For the equations to be multiples of each other, the ratios of the coefficients of , , and the constants must be equal. This gives the following system of equations:

Step 3: Solving for .
First, simplify the ratio : Now, solve for by equating to : Cross-multiply:

Step 4: Conclusion.
Thus, for the system to have infinite solutions,