Question

x2 + y2 = 8
x - y = 0

Select all of the following that are solutions to the system shown.

(2, 2)
(2, -2)
(-2, 2)
(-2, -2)

Answer 1

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(x-y)^2=0^2


x^2-2x.y+y^2=0


8-2x.y=0


2x.y=8


x.y=4

(-2). (-2)=4

2.2=4


x-y=-2-(-2)= -2+2=0


x-y=2-2=0


(-2,-2)

(2,2)

Answer 2

Answer:  The answer are (a) (2, 2) and (d) (-2, -2).

Step-by-step explanation:  The given system of equations is

$x^2+y^2=8,~~~~~~~~~~~~(A)\\\\x-y=0.~~~~~~~~~~~~~~~(B)$

We are to select all the correct options from the given that are solutions to the above system.

Let us solve the system of equations as follows:

From equation (B), we have

$x-y=0\\\\\Rightarrow x=y.~~~~~~~~~~~(C)$

Using equation (C) in equation (B), we have

$x^2+y^2=8\\\\\Rightarrow x^2+x^2=8\\\\\Rightarrow2x^2=8\\\\\Rightarrow x^2=4\\\\\Rightarrow x=\pm2,$

and from (C) again, we get

$y(x=2)=2,\\\\y(x=-2)=-2.$

Therefore, the solutions are (2, 2) and (-2, -2).

Thus, (a) and (d) are the correct options.