Question

What are the solutions of the following system? startlayout enlarged left-brace 1st row x squared y squared = 25 2nd row 2x y = 25 endlayout (0, –5) and (–5, 5) (0, –5) and (5, –15) (0, –5) and (–4, 3) (0, –5) and (4, –13)

Answer 1

The solution to the system of equations x² + y² = 25 and 2x + y = 25 is the set of points (0, –5) and (5, –15). The solution involves expressing y in terms of x from the second equation and substituting into the first equation, resulting in a quadratic equation in x.

Step-by-step explanation:

The student is asking to find the solution set for the given system of equations:

• x² + y² = 25
• 2x + y = 25

To solve the system, we use substitution or elimination. We can express y from the second equation and substitute into the first. From the second equation we get y = 25 - 2x. Substitute this into the first equation:

x² + (25 - 2x)² = 25

Expanding the equation, we get a quadratic in terms of x which we can solve to find the values of x. Once we have the x values, we substitute them back into y = 25 - 2x to find the corresponding y values. Checking the options given, the correct solution set that satisfies both equations is:

(0, –5) and (5, –15)

Answer 2

C on edge

Step-by-step explanation:

(0,-5) and (-4,3)