Final answer:
To have an infinite number of solutions, the two equations in the system must be equivalent. The values of a = 1 and c = -2 would result in an infinite number of solutions.
Step-by-step explanation:
To have an infinite number of solutions, the two equations in the system must be equivalent. In other words, the left sides of the equations need to be multiples of each other and the right sides need to be equal.
To find the values of a and c that satisfy this condition, we can set up an equation by equating the ratios of the coefficients:
-2/a = 1/-2
Solving this equation, we find that a = 1. Since the value of a is now known, we can substitute it back into one of the original equations to find c. Let's choose the second equation:
1x - 2y = c
Substituting a = 1 and using the value -2 for y from the first equation, we find c = -2.
Therefore, the values for a and c that would result in an infinite number of solutions are a = 1 and c = -2.
Learn more about infinite solutions