Answer:
Option A
A) (-3,-4) (4,3)
Step-by-step explanation:
We have a system of equations composed of:
The equation of a circle that has center at point (0,0) and radius r = 5.
The equation of a line that intercepts the y-axis at point (0,1)
To solve the system we substitute the equation of the line in the equation of the circumference:
[tex]y = x - 1\\\\x ^ 2 + y ^ 2 = 25[/tex]
Then
[tex]x ^ 2 + (x-1) ^ 2 = 25[/tex]
We solve for x.
[tex]x ^ 2 + x ^ 2 -2x +1 = 25\\\\2x ^ 2 -2x -24 = 0[/tex]
We divide by 2 both sides of the equation
[tex]x^2 -x -12 = 0[/tex]
We look for two numbers that multiply as a result -12 and that add them as a result -1.
These numbers are -4 and 3.
Therefore the factors are:
[tex](x-4) (x + 3) = 0[/tex]
Finally the solutions are:
[tex]x = 4[/tex] and [tex]x = -3[/tex]
The ordered pairs are:
(-3,-4) (4,3)
