Final answer:
When a system of equations has no solution, the lines are parallel and never intersect. The slope of the second equation in this case is equal to a/b, which we can find by cross multiplying and dividing. The value of a/b is 4/3.
Step-by-step explanation:
When a system of equations has no solution, it means that the lines represented by the equations are parallel and never intersect. In this case, the two equations are 3/4x - 1/2y = 12 and ax - by = 9.
Since these lines are parallel, their slopes are equal. The slope of the first equation is 3/4 and the slope of the second equation is a/b. Therefore, 3/4 = a/b.
To find the value of a/b, we can cross multiply: 3/4 * b = a. Multiplying both sides of the equation by 4, we get: 3b = 4a. Dividing both sides of the equation by 3, we find that a/b = 4/3.
Therefore, the value of a/b is 4/3. Option A) 2/3 is incorrect as it does not match the calculated value.