Choose all ordered pairs that are solutions of the system:
x^2-x+y^2=21 & x+3y=2

(1,5) (5,-1) (-4,2) (-3,2)

Question

Choose all ordered pairs that are solutions of the system:
x^2-x+y^2=21  &  x+3y=2

(1,5)  (5,-1)  (-4,2)  (-3,2)

mysesshou · Answer

I think I would substitute the second equation into the first and solve for one of the variables. Then solve for the others.  Do you need help doing that?

mysesshou · Answer

By substituting the values into the second equation, only the middle two pairs fit the second equation, but you can use the second equation and plug it into the first.

actually, you can just plug the pairs into both equations and only choose the pairs in both equations.

anonymous · Answer

You dont have to add the equations together. you just plug the pairs into the equation.

anonymous · Answer

and the pair has to work for both equations.

mysesshou · Answer

by substituting the equations you can solve them at once, but plugging in the points is also possible.

substituting in the pairs might be simplest. 
(1,5) 
1^2-1+5^2 does not =21     X
1+3*5 does not =2              X

 (5,-1) 
5^2-5+(-1)^2=21       yes
5+3(-1)=2                   yes

(-4,2)  
(-4)^2-(-4)+2^2  does not=21     X
-4+3*2=2          yes

 (-3,2)
(-3)^2+3+2^2  does not=21   X
-3+3*2 does not=2     X

sorry, type slow.  :)