Answer: y = 2 and x = 2
Step-by-step explanation:
[tex]9x^2+4(y-2)^2=36\\x^2=2y[/tex]
First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y
[tex]9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0[/tex]
What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.
[tex]4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2[/tex]
Now solve for x by plugging in y to the easier equation
[tex]x^2=2(-5/2)\\x\neq \sqrt{-5}[/tex]
If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2
[tex]x^2=2(2)\\x=2[/tex]
