Question 4(Multiple Choice Worth 1 points) (05.03 MC) Determine which system will produce infinitely many solutions.

To produce infinitely many solutions in a system of equations, the equations must represent the same line when graphed. This generally happens when the equations are equivalent, meaning that one can be derived from the other by multiplying or dividing by a non-zero constant. For example, if you have two equations, such as \(2x + 4y = 8\) and \(x + 2y = 4\), they are essentially the same line—which reveals a delightful continuum of solutions! To spot these situations, always look for the coefficients of \(x\) and \(y\) to be proportional across the equations. Common mistakes include miscalculating the coefficients or the constants, leading to false conclusions of no solutions or a unique solution. A quick check by rearranging the equations can aid in accurately identifying infinite solutions!