Question

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​

Answer 1

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

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.

Answer 2

a = 4

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.