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Mathematics 32 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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...

OpenStudy (anonymous):

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

OpenStudy (anonymous):

hmmm i dont know..sorry im really confused

OpenStudy (anonymous):

Can you expand this: (2x−1)² = ....

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

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

OpenStudy (anonymous):

trying to follow

OpenStudy (anonymous):

(2x−1)² = ....

OpenStudy (anonymous):

hold on

OpenStudy (anonymous):

4x^2-4x+1

OpenStudy (anonymous):

Great :) x² + 4x² - 4x + 1 -4 = ....

OpenStudy (anonymous):

5x^2-4x-3

OpenStudy (anonymous):

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

OpenStudy (anonymous):

hint please? sorry

OpenStudy (anonymous):

Δ = b² - 4ac

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ok and how do you find the intersection from that?

OpenStudy (anonymous):

x = ( -b ± √Δ ) / 2a

OpenStudy (anonymous):

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

OpenStudy (anonymous):

thank you!!!! so helpful

OpenStudy (anonymous):

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

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