Final answer:
To find one solution of the given system, we can solve the equations simultaneously using the substitution method. The solutions to the system are (0, 6) and (-6, 0).
Step-by-step explanation:
To find one solution of the given system, we need to solve the two equations simultaneously. Let's solve the system using substitution method:
1. Rearrange the first equation to solve for y:
y = (2/2)x + 6
y = x + 6
2. Substitute this value of y into the second equation:
x^2 + (x + 6)^2 = 36
3. Simplify and solve the quadratic equation:
x^2 + x^2 + 12x + 36 = 36
2x^2 + 12x = 0
x(x + 6) = 0
4. Set each factor equal to zero and solve:
x = 0 or x = -6
5. Substitute these values of x into the first equation to find the corresponding y-values:
For x = 0: y = (2/2)(0) + 6 = 6
For x = -6: y = (2/2)(-6) + 6 = 0
Therefore, the solutions to the system are (0, 6) and (-6, 0).