Solve for X

1) (x-5)^2+(y+3)^2=0
if x and y are real numbers then
(x-5)^2=0 and (y+3)^2=0
why? nuttin plus nuttin is nuttin
and x=5 and y=-3 so your right here
on a real coordinate space the coordinate pair solution (x,y) is (5,-3)

2) (x^2+4)(2y+3)=0
of x and y are real then if y=-3/2
the (x^2+4)(0)=0 for any real x
on a real coordinate space the solution is a horizontal line where y=-3/2


There are other solutions if x is a complex number. A complex number includes a real and an imaginary part. such that x=a+bi, in this case a solution for x is a=o and b-2 so x=2i and since i^2=-1 then x^2=-4 and -4+4=0 and y can be any complex number.

Note with complex numbers if b=0 then the number is real

Rap

My grading rubric
7.1 2 points--there are two real solutions. one point for each solution
7.2 4 points--one point for recognizing that if AB=0 then A=0 or B=0--second point for the real solution for y for any real x--additional points for recognizing the complex nature of solutions for x (1 for seeing that x^2=-4 has no real solution and the other for recognizing imaginary/complex solution for x)

Rap

We don't allow fractions here.

bm

Red888,

Can you check if there is a misprint in 7.1 please ?

These look to me like a pair of simultaneous quadratics, but substituting y=-1.5 in the first equation gives complex roots.

No, I don't think it's a misprint. There are two simultaneous quadratics, question 8 and 9. This is a mixed worsheet so they don't usually have more than 2 of the same type of question. Ok thanks alot for your help all.

Red888,

...then it is hard to see the "teaching principle" behind such examples....the first is a degenerate circle centre (5,-3) and the second, as our friends have said involves complex numbers.

BTW heres an interesting link which allows you to play with equations and watch them on a graph.

http://descartes.cnice.mecd.es/ingles/Bach_CNST_1/Simultaneous_equations_inequations/Sistemas_ecuaciones.htm

Try inserting the first equation in the last example and then alter the "0" answer to 1, 2, 3 etc....

They were probably trying to make us "think". Well I appreciate the help. Thanks for the link too.