<PRE><B>Question 1007316</B>
 Given the equation of the circle x^2 + y^2 = 25 and 
 the equation of the line 2x + y = 10... 
 Find the solutions algebraically
:
One way is write the 2nd equation as
y = -2x + 10
Substitute for y in the 1st equation
x^2 + (-2x+10)^2 = 25
FOIL (-2x+10(-2x+10)
x^2 + (4x^2 - 20x -20x + 100) = 25
Combine like terms
x^2 + 4x^2 - 40x + 100 - 25 = 0
5x^2 - 40x + 75 = 0
Simplify, divide by 5
x^2 - 8x + 15 = 0
Factors to
(x-5)(x-3) = 0
Two solutions
x = 5
x = 3
:
Using the equation y = -2x+10, find y using both x solution
y = -2(5) + 10
y = 0 
and
y = -2(3) + 10
y = -6 + 10
y = 4
:
Solutions: 
 x=5; y=0
 x=3; y=4
:
Check in the 1st equation using the last pair, (the first pair is obvious)
3^2 + 4^2 = 25
9 + 16 = 25
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