What is the solution set to the following system?enlarged left-brace Start Layout 1st row x plus y equals 5 2nd row x squared plus y squared equals 25 End Layout
The solution set to the system of equations is:
{(3,2), (-3,-2)}
Are you sure
I apologize for the mistake. The correct solution set for the system of equations is:
{(3, 4), (4, 3), (-3, -4), (-4, -3)}
I don't think that's right either
I apologize for the incorrect response. Let's solve the system of equations again.
From the first equation, we have:
x + y = 5
From the second equation, we have:
x^2 + y^2 = 25
We can solve this system by substitution. Rearranging the first equation, we have:
y = 5 - x
Substituting this into the second equation, we get:
x^2 + (5 - x)^2 = 25
Expanding and simplifying:
x^2 + (25 - 10x + x^2) = 25
2x^2 - 10x = 0
2x(x - 5) = 0
Setting each factor equal to zero:
2x = 0 or x - 5 = 0
Solving for x:
x = 0 or x = 5
If x = 0, substituting into the first equation we get:
0 + y = 5
y = 5
So one solution is (0, 5).
If x = 5, substituting into the first equation we get:
5 + y = 5
y = 0
So another solution is (5, 0).
Therefore, the solution set to the system of equations is:
{(0, 5), (5, 0)}