Question

X² + y² = 8

x - y = 0
Select all of the following that are solutions to the system shown.
O (2, 2)
O (2,-2)
O (-2,2)
0 (-2,-2)

Answer 1

`(2,2)~ \text{and}~ (-2,-2)`

Step by step explanation:

`x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \frac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \frac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\`

`\text{Hence,}~ (x,y) = (\pm2, \pm 2)`