1. ## Intersection(s) between equations

What is the intersection between:
x^2+y^2=25
-3x+y=15

i got (-5/2 , -15/2) & (-10,-15) is that right or wrong?

2. plug your points into the original two equations. If they satisfy them both, then they are points of intersection.

3. i got it wrong then...

4. Originally Posted by jordangiscool
What is the intersection between:
x^2+y^2=25
-3x+y=15

i got (-5/2 , -15/2) & (-10,-15) is that right or wrong?

If x= -5/2 and y= -15/2 then 3x+ y= 3(-5/2)+ (-15/2)= -30/2= -15 so that is correct. [tex]x^2+ y^2= (-5/2)^2+ (-15/2)^2= 25/4+ 225/4= 250/4= 62.5[tex]. No, that's not correct.

If -3x+ y= 15, then y= 15+ 3x. Putting that into the first equation gives $\displaystyle x^2+ (15+ 3x)^2= x^2+ 225+ 90x+ 9x^2= 25$ or $\displaystyle 10x^2+ 90x+ 200= 0$ which, dividing by 10, is the same as $\displaystyle x^2+ 9x+ 20= 0$. Can you solve that? Does it have any real solutions? It is possible that the line completely misses the parabola.