Answer :
Step-by-step explanation:
Since the system has only one solution, the quadratic equation must have only one root. This means that the discriminant (b^2 - 4ac) is equal to zero.
In this case, the equation is y = x^2 + 8x + a, so we can plug in the values as follows:
b^2 - 4ac = 0
(8)^2 - 4(1)(a) = 0
64 - 4a = 0
4a = 64
a = 16
So, the value of a is 16.
Note that we can also find the value of a by substituting the value of y (-1.5) into the equation and solving for a:
-1.5 = x^2 + 8x + a
x^2 + 8x + a = -1.5
Since there is only one solution, we know that the quadratic equation must have only one root, which means that the discriminant is equal to zero. Solving for a, we get the same result: a = 16.
