Question 973399
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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