Final answer:
Algebraic solution to a system of equations involving a circle and a line.
Step-by-step explanation:
The subject of this question
is Algebra. We have two equations in two variables, x and y. The first equation, (x + 2)² + y² = 85, represents a circle centered at (-2,0) with a radius of √85. The second equation, x+y=9, represents a line in the xy-plane. The solution to this system of equations is the point(s) where the line intersects the circle, if any.
To solve the system, we can substitute the value of y from the second equation into the first equation:
(x + 2)² + (9-x)² = 85.
Expanding, simplifying, and solving this equation will give us the values of x and y which satisfy both equations.
Learn more about System of equations, algebra