# Simultaneous Equations

• Nov 22nd 2009, 07:07 AM
Mukilab
Simultaneous Equations
Just a simultaneous equation I've found and need help on.

x^2 + y^2 = 5
y = 3x + 1

• Nov 22nd 2009, 07:21 AM
skeeter
Quote:

Originally Posted by Mukilab
Just a simultaneous equation I've found and need help on.

x^2 + y^2 = 5
y = 3x + 1

substitute for y and solve ...

\$\displaystyle x^2 + (3x+1)^2 = 5\$

you'll get two solutions where the line intersects the circle.
• Nov 22nd 2009, 07:36 AM
Mukilab
did that and got a 9x^2 before....

Confused how to get the final product. That's kind of what I was asking for?
• Nov 22nd 2009, 07:45 AM
skeeter
Quote:

Originally Posted by Mukilab
did that and got a 9x^2 before....

Confused how to get the final product. That's kind of what I was asking for?

\$\displaystyle x^2 + (3x+1)^2 = 5\$

\$\displaystyle x^2 + 9x^2 + 6x + 1 = 5\$

\$\displaystyle 10x^2 + 6x - 4 = 0\$

\$\displaystyle 5x^2 + 3x - 2 = 0\$

factor and solve.
• Nov 22nd 2009, 07:48 AM
Mukilab
thank you