Find a point in the xy plane that the first coordinate...HELP ME?

Question

Find a point in the xy plane that the first coordinate plus the second coordinate equals 3, and the square of the first coordinate minus the square of the second coordinate equals -9.

Alright, basically I keep coming up with x=3, which would make y=0. Please help me, I'm really frustrated with this problem.

Answer 1

x + y = 3 solving for y: y = 3 - x
x^2 - y^2 = -9
substituting 3-x in for y
x^2 - (3-x)^2 = -9
x^2 - 9 +6x - x^2 = -9
6x - 9 = -9
6x = 0
x = 0
going back to the original equations
0 + y = 3
y = 3

Answer 2

I think you are right but X should be 0 and Y=3 so the first coordinate minus the square of the second coordinate equals -9

Answer 3

I hope you're comfortable with algebra and linear equations.
Here you get two equations:
equation 1 : x + y = 3 and
equation 2 : x^2 - y^2 = -9

Expanding equation 2 we have:
equation 3: (x+y)(x-y) = -9
But from equation 1 we have x + y = 3
So, equation 3 becomes: 3(x - y) = -9
=> x - y = -9/3 = -3
Let us call this equation 4.

Solving equations 1 and 4 we get:
x + y = 3
x - y = -3
=> 2x = 0
=> x = 0
And hence: y = 3.
That's your coordinate: (x,y) = (0,3).

Answer 4

I think you are right.

x + y = 3
x^2 - y^2 = -9

Factor the second eq:

(x + y)*(x - y) = -9

Substitute the (x + y) from the first:

3*(x - y) = -9

Now we have two first-order equations in two unknowns:

x + y = 3
x - y = -3

Add them to get 2x = 0, x = 0; put that back into either to get y = 3

There is nothing unusual about having one coordinate equal to zero; in fact, both coordinates can be zero (that is the origin).

Answer 5

Hey, okay, so the easiest way to do this question is to write out the two equations you are given.
(k just for notation sake, x^2 is x squared. y^2 is y squared, ok?)
eq. 1) x+y=3
eq. 2) x^2 - y^2 = -9

take eq. 1 and solve for x,
x=3-y
sub that into eq.2
(3-y)^2 - y^2 - -9
use foil on the first term to get
9-6y+y^2 - y^2 = -9
collect like terms
9-6y= -9
move the 9s to the same side and divide by six, you get
y=3
sub into eq.1
x+3=3
x=0
check with eq. 2
0^2 - 3^2 = -9
that is true therefore you are all finished!!!
good luck!

Answer 6

swap it. x=0 and y=3

0+3=3. right? right.

0*0=0 right? right.

3*3=9 right? right.

0-9=-9. you're close. just keep it simple.