2nd degree equations??

Question

solve the system

x^2 - y^2 = 9

y^2 - 2x = 6

i need solutions thanks

Answer 1

Subtract them from each other to get:

x^2 - 2x = 3

Move 3:

x^2 - 2x -  3 = 0

Use quadratic formula to solve for x, and plug x values back in an original equation to find y values.

Answer 2

Add them to get x^2 - 2x = 15

so x^2 - 2x +1 = 16 which means (x -1) = 4 or -4. so x = 5 or -3.The you can caculate y for these values of x

Answer 3

x² - y² = 9

y² = x² - 9

y² - 2x = 6

y² = 2x + 6

Value of x:

x² - 9 = 2x + 6

x² - 2x = 15

x² - x = 15 + 1

(x - 1)² = 16

x - 1 = 4

x = 5

Value of y:

y² = 5² - 9

y² = 25 - 9

y² = 16

y = 4

Answer: x = 5, y = 4

Proof (1st equation):

5² - 4² = 9

25 - 16 = 9

9 = 9

Proof (2nd equation):

4² - 2(5) = 6

16 - 10 = 6

6 = 6

Answer 4

hi

y^2-2x=6  ==>

y^2=6+2x

x^2-y^2=9  ==>add them

x^2-2x-3=0 ==> ==>

(x-3)(x+1)=0

x=3  ,  x=-1