Question 86878: please solve this problem: find the points of intersection of the straight line 7x+y=25 and the circle x^2+y^2=25
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! please solve this problem: find the points of intersection of the straight line 7x+y=25 and the circle x^2+y^2=25
:
7x + y = 25
y = (25-7x)
:
Substitute (25-7x) for y in circle equation (x^2 + y^2 = 25):
x^2 + (25-7x)^2 = 25
:
x^2 + 625 - 350x + 49x^2 = 25; FOILed (25-7x)(25-7x)
:
x^2 + 49x^2 - 350x + 625 - 25 = 0; combine like terms
:
50x^2 - 350x + 600 = 0; a quadratic equation
:
Simplify, divide equation by 50:
x^2 - 7x + 12 = 0
:
Factors to:
(x-3)(x-4) = 0
x = +3
and
x = +4
:
Substitute these x values in y = 25-7x to find points of intersection:
y = 25 - 7(3)
y = 25 - 21
y = +4
:
First point of intersection: 3,4
:
y = 25 - 7(4)
y = 25 - 28
y = -3
:
2nd point of intersection: 4,-3
:
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