Consider the system of linear equations: ax+y=b 16x+ay=24 Suppose the values…

For a system of linear equations to have multiple (infinite) solutions, the ratios of corresponding coefficients must be equal.

Given: ax + y = b and 16x + ay = 24. Condition: a/16 = 1/a = b/24.

From a/16 = 1/a, we get a^2 = 16, so a = ±4. From 1/a = b/24, we get b = 24/a.

Product ab = a * (24/a) = 24. Thus, the product of a and b is 24.