solve by substitution or elimination:
x^2+y^2=25 and x^2-y^2=7

Question

solve by substitution or elimination:
x^2+y^2=25 and x^2-y^2=7

hero · Answer

add them together

anonymous · Answer

$$x ^{2}+y ^{2}=25$$
$$x ^{2}-y ^{2}=7$$
Add both equation we get 
$$2x ^{2}=32$$
implies  $$x ^{2}=16$$
x=+4 or -4

anonymous · Answer

they want ordered pairs as solutions.

anonymous · Answer

they want you to plug positive 4 back into one of the original equations and solve. same with the -4.

anonymous · Answer

what would that come out to be because im not getting the correct numbers?

anonymous · Answer

oh sorry i didn't completed the work

anonymous · Answer

Solution (x,y)=(4,3),(-4,3),(4,-3)

whpalmer4 · Answer

Using the second equation:
$$4^2-y^2=7$$$$16-7=y^2$$$$y=\pm\sqrt{9} = \pm3$$
$$(-4^2-y^2=7)$$$$16-7=y^2$$$$y=\pm3$$
Solutions are (4,3),(-4,3),(4,-3),(-4,-3)

whpalmer4 · Answer

Sorry, I didn't get the parens in the right place, that should be $$(-4)^2-y^2=7$$but the outcome is the same.

anonymous · Answer

mr.whpalmer4 i forget to write (-4,-3)

anonymous · Answer

I'm confused about how it is 4 solutions, because plugging it in you don't get those. I'm not getting them.

anonymous · Answer

if $$x ^{2}=a$$ then the solutions are +a or -a

anonymous · Answer

isn't the answer just + or - 4, and + or - 3?

anonymous · Answer

without writing the ordered pairs? isn't it the same thing?

anonymous · Answer

ordered pair used is to ensure the order

anonymous · Answer

That makes more sense. thank you so much Joseph, whpalmer, and Hero :)