Answer:
To find the value of $a$ for which the given system of equations has no solutions, we need to check if the lines represented by the equations are parallel. If the lines are parallel, they will never intersect, resulting in no solution to the system.
First, let's rewrite the second equation in slope-intercept form:
$2y-4 = ax + y - 6$
This can be simplified as:
$y = (ax + y) - 2$
$y = ax + y - 2$
$0 = ax - 2$
From this, we can observe that the second equation represents a line with the slope $a$ and the y-intercept at -2.
Comparing this with the equation $y = 11x + 14$, we can see that the slope of the first equation is 11.
For two lines to be parallel, their slopes must be equal. Therefore, to have no solutions, we need to find the value of $a$ that makes the slopes of the two lines equal.
Setting the slopes equal, we have:
$11 = a$
Thus, the value of $a$ that will result in no solutions to the system of equations is $a = 11$.