Question

X² + y² = 34
x + y =8​

Answer 1

Explanation:

`{x}^(2) + {y}^(2) = 34 \\ x + y = 8 \\ x = 8 - y \\ substitute \: x \: in \\ {x}^(2) + {y}^(2) = 34 \\ {(8 - 4)}^(2) + {y}^(2) = 34 \\ {(8 - 4) }^(2) = {y}^(2) - 16y + 64 \\ {y}^(2) - 16y + 64 + {y}^(2) = 34 \\ {2y}^(2) - 16y + 64 = 34 \\ {2y}^(2) - 16y + 64 - 34 = 0 \\ {2y}^(2) - 16y + 30 = 0 \\ 2 {y}^(2) - 6y - 10y + 30 = 0 \\ (2 {y}^(2) - 6y) - (10y + 30) = 0 \\ 2y(y - 3) - 10(y - 3) = 0 \\ (2y - 10)(y - 3) \\ 2y = 10 \\ y = (10)/(2) \\ y = 5 \\ or \\ y = 3 \\ if \: y = 5 \: \: x = 3 \\ if \: y = 3 \: \: x = 5`