solve the simultaneous equation x+y=2 and x^2+2y=12

Question

solve y and x

Answer 1

1).  x + y = 2

2).  x^2 + 2y = 12

in equation 1). solve for y.

1a). y = 2 - x

substitute into equation 2).

x^2 + 2(2 - x) = 12

x^2  - 2x + 4 = 12

x^2 - 2x -8 = 0

(x - 4)(x + 2) = 0

x equals x = 4 or x = -2

plug into equation 1)

x + y = 2              

4 + y = 2                   or           -2 + y = 2

y = -2                        or             y =  4 in x,y notation the answers look like this:

(4, -2)                        or          (-2, 4)

check answers in equation 2)

x^2 + 2y = 12

4^2 + 2(-2) = 12                                    or               (-2)^2 + 2(4) = 12

8 -4 = 12         NO!!!                             or               4 + 8  = 12

(4, -2) is not an answer.  The answer is (-2, 4).

 

 

Answer 2

y sin 45 = 5 cos u

-y cos 45 = -2 - 5 sin u