Specify the value of the product x1y1, if it is known that (x1y1) is the solution to the system

Specify the value of the product x1y1, if it is known that (x1y1) is the solution to the system of equations: x + y = 1, y ^ 2-x ^ 2 = 5

From the first equation of this system, we get that

y = 1 – x.

Substitute this value for y into the second equation and get:

(1 – x) ² – x² = 5,

1 – 2 * x + x² – x² = 5,

1 – 2 * x = 5,

2 * x = -4,

x = -2.

Therefore, y = 1 – (-2) = 1 + 2 = 3.

Thus, the solution to this system is a pair of numbers -2 and 3, and from the product is equal to:

-2 * 3 = – 6.

Answer: -6.