# Thread: (SIMULTANEOUS) How to solve 4x+12=x^2+8y^2=2y+5x+6

1. ## (SIMULTANEOUS) How to solve 4x+12=x^2+8y^2=2y+5x+6

Solve it without a GC.

Answers given: x=6, y=0 or x=10/3, y=4/3

I got the 2nd set of answers but i can't seem to get x=6 and y=0

Please help me thank you! If possible please include explanation. Once again, thank you

2. ## Re: (SIMULTANEOUS) How to solve 4x+12=x^2+8y^2=2y+5x+6

Originally Posted by pumbaa213
Solve it without a GC.

Answers given: x=6, y=0 or x=10/3, y=4/3

I got the 2nd set of answers but i can't seem to get x=6 and y=0

Please help me thank you! If possible please include explanation. Once again, thank you
$4x+12=2y+5x+6 \Rightarrow y=\frac{6-x}{2}$

$4x+12=x^2+8y^2 \Rightarrow 4x+12=x^2+8\left(\frac{6-x}{2}\right)^2 \Rightarrow$

$4x+12=3x^2-24x+72 \Rightarrow$

$3x^2-28x+60=0 \Rightarrow$

$(x=6) or \left(x=\frac{10}{3}\right)$

$x=6 \Rightarrow y=0 and x=\frac{10}{3} \Rightarrow y=\frac{4}{3}$

3. ## Re: (SIMULTANEOUS) How to solve 4x+12=x^2+8y^2=2y+5x+6

Thank you so much once again!