Solving Systems of Equalities

[diamondsintherough]

Someone please help me. I found only one set of answers for this problem, but there are two. How do I find the second set?

x + 3y = 5
x^2 + y ^2 = 25

One solution set is (5,0). That one I can find. How do I get this second answer, which is from my answer key: (-4,3)

Thanks, math tutors.

 

[Loren]

There are different approaches. Here's one approach.

Solve the linear equation for x getting x=5-3y.
Plug that into the other equation getting (5-3y)[sup:31avd0gp]2[/sup:31avd0gp] + y[sup:31avd0gp]2[/sup:31avd0gp] = 25.
Solve that equation for y and you should get two possible values for y.
Plug each of those values (one at a time) back into the linear eqn. to get both solutions.

 

[diamondsintherough]

Thank you! I should have known that... I appreciate your quick response!

 

[diamondsintherough]

Wait. I already did exactly that. And I got y = 0. How did they get y = -3 ??