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8090 [49]
3 years ago
15

X² + y² = 34x + y =8​

Mathematics
1 answer:
Nataly [62]3 years ago
4 0

Step-by-step 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  = \frac{10}{2}  \\ y = 5 \\ or \\ y = 3 \\ if \: y = 5 \:  \: x = 3 \\ if \: y = 3 \:  \:  x = 5

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