Pre calculus

Question

X² + y² =10

x+y =1

Answer 1

x² + y² = 10

x + y = 1

 

Since x + y = 1, y = 1 - x

 

Replace y by 1 - x in the first equation:  x² + (1 - x)² =10

 

x² + 1 - 2x + x² = 10

 

2x² - 2x - 9 = 0

 

x = (2 ± √[(-2)² - 4(2)(-9)])/4

 

   = (2 ± √76)/4

 

   = (2 ± 2√19)/4

 

    = (1 ± √19)/2

 

If x = (1 + √19)/2, then y = 1 - x = (1 - √19)/2

If x = (1 - √19)/2, then y = 1 - x = (1 + √19)/2