Final answer:
To find the value of b for which the given equations will have infinite solutions, we can set the coefficients of x and y proportional in both equations. The value of b that satisfies this condition is 54.
Step-by-step explanation:
To find the value of b for which the given equations will have infinite solutions, we need to look for a condition where the two equations are equivalent. In other words, the two equations should represent the same line. This can be achieved by setting the coefficients of x and y in both equations proportional.
If we compare the coefficients of x and y in the given equations, we can see that the ratio of coefficients of x is 2 to 27, while the ratio of coefficients of y is 4 to 2(27). Simplifying, we get the condition 2/27 = 4/(2(27)). Solving this equation, we find that b = 54.