please help me solve an equation!?

Question

y=2x+1
x^2+y^2=13

thank you for you help - i had been multiplying out the brackets wrong

Answer 1

y=2x+1
x^2+y^2=13

substitute the 1st into the 2nd eq.
x^2 + (2x+1)^2 = 13
x^2 + 4x^2 + 4x + 1 = 13
5x^2 + 4x-12 =0
x= ( -4 +- sqrt( 16 - 20(-12) ) )/10

Answer 2

you have a line, y = 2x + 1, intersecting a circle, x² + y² = 13, at 2 points. replace y² with (2x+1)²:

x² + (2x+1)² = 13
x² + 4x² + 4x + 1 = 13
5x² + 4x - 12 = 0
(5x - 6)(x + 2) = 0
x = 6/5, y = 2(6/5) + 1 = 17/5
x = -2, y = 2(-2) + 1 = -3