find the coordinates of the points of intersection for the graphs of x^2+y^2=4 and y=2x-1

Question

anonymous · Answer

the first equation is that of a circle and the other one is that of a line...
so at most there are 2 intersections (or solutions to this system of equations....

substitute the second equation into the first equation...

anonymous · Answer

$$\large x^2+y^2=4,\space y=2x-1\rightarrow  x^2+(2x-1)^2=4 $$
can you solve that?

anonymous · Answer

hmmm i dont know..sorry im really confused

anonymous · Answer

Can you expand this:
(2x−1)² = ....

anonymous · Answer

solve the equation:
$$\large x^2+(2x-1)^2=4  $$
$$\large x^2+(2x-1)(2x-1)=4$$

anonymous · Answer

ok

anonymous · Answer

@kenneyfamily what do you mean by "ok" ???

anonymous · Answer

trying to follow

anonymous · Answer

(2x−1)² = ....

anonymous · Answer

hold on

anonymous · Answer

4x^2-4x+1

anonymous · Answer

Great :)
x² + 4x² - 4x + 1 -4 = ....

anonymous · Answer

5x^2-4x-3

anonymous · Answer

Can you find intersection x by solving quadratic equation:
5x²-4x-3 = 0

anonymous · Answer

hint please? sorry

anonymous · Answer

Δ = b² - 4ac

anonymous · Answer

b = -4, a = 5, c= -3

anonymous · Answer

ok and how do you find the intersection from that?

anonymous · Answer

x = ( -b ± √Δ ) / 2a

anonymous · Answer

Then plug x value into y = 2x -1 to get y value!

anonymous · Answer

thank you!!!! so helpful

anonymous · Answer

@kenneyfamily I hope you look back your previous post to find my answers to learn! 
It'll benefit for your further learning!