14. A system of equations is shown below. For what value of a will this system have no solutions? Justify your answer. y = 4x-9
y = ax+6​

a = 4

Step-by-step explanation:

a = 4

If a = 4, then both lines have the same slope and different y-intercepts. That makes both lines parallel. Since the lines never intersect, there is no solution.

x can not equal zero, as it would cause division by zero.

Step-by-step explanation:

First, let's make one equation out of them and see what we get.  Because both of them have y on the left, we can say that the two right sides are equal, giving us:

4x - 9 = ax + 6

If we solve for a, we get:

ax + 6 = 4x - 9

ax = 4x - 15

a = 4 - 15 / x

With that arrangement we can see clearly that x can not be equal to zero, as it would give us division by zero.

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step-by-step explanation:

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