Question

X^2 + y^2 = 10
y = x - 2

Find x and y

Answer: ( , )
( , )

Answer 1

`{x}^(2) + {(x - 2)}^(2) = 10 \\ \\ {x}^(2) + (x - 2)(x - 2) = 10 \\ \\ {x}^(2) + {x}^(2) - 4x + 4 = 10 \\ 2 {x}^(2) - 4x + 4 - 10 = 0 \\ 2 {x}^(2) - 4x -6 = 0 \\ 2( {x}^(2) - 2x - 3) = 0`

DIVIDE THE WHOLE EQUATION BY 2 TO GET

`{x}^(2) - 2x -3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1`

WHEN x=3

`y = 3 - 2 \\ y = 1`

when x=-1

y=-1-2

y=-3

SOLUTIONS NOW CAN BE

(3,1) AND (-1,-3)