SOLUTION: can someone help me please? thanks! and show work as well please :) Find the point(s) of intersection of the line X + Y = 5 and the circle x2 + y2 = 25 by solving the system of

Algebra ->  Points-lines-and-rays -> SOLUTION: can someone help me please? thanks! and show work as well please :) Find the point(s) of intersection of the line X + Y = 5 and the circle x2 + y2 = 25 by solving the system of       Log On


   

Question 973399: can someone help me please? thanks! and show work as well please :)
Find the point(s) of intersection of the line X + Y = 5 and the circle x2 + y2 = 25 by solving the system of equations.

Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
x + y = 5 ----> x = -y + 5 {subtracted y from each side of top equation}
x² + y² = 25

(-y + 5)² + y² = 25 {substituted (-y + 5), in for x, into bottom equation}
y² - 10y + 25 + y² = 25 {squared the binomial using the foil method}
2y² - 10y + 25 = 25 {combined like terms}
2y² - 10y = 0 {subtracted 25 from each side}
2y(y - 5) = 0 {factored out the greatest common factor, 2y}
2y = 0 or y - 5 = 0 {set each factor equal to 0}
y = 0 or y = 5 {divided each side of 1st equation by 2 and added 5 to each side of 2nd equation}

x + y = 5 {first original equation}
If y = 0
x + 0 = 5 {substituted 0 for y}
x = 5 {subtracted 0 from each side}
(5,0) is a solution}

If y = 5
x + 5 = 5 {substituted 5 for y}
x = 0 {subtracted 5 from each side}
(0,5) is a solution

The line will intersect the circle at (0,5) and (5,0)
x = 5 and y = 0
or
x = 0 and y = 5

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