SOLUTION: what is the point of intersection of the following systems of equations algebraically? xy=8 x+y=6

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 Question 38924: what is the point of intersection of the following systems of equations algebraically? xy=8 x+y=6Found 2 solutions by AnlytcPhil, fractalier:Answer by AnlytcPhil(1276)   (Show Source): You can put this solution on YOUR website!```What is the point of intersection of the following systems of equations algebraically? xy = 8 x + y = 6 Method: substitution. Solve the second equation for y y = 6 - x Substitute (6 - x) for y in the first equation xy = 8 x(6 - x) = 8 6x - x² = 8 Get 0 on the left 0 = x² - 6x + 8 0 = (x - 2)(x - 4) Use the zero-factor property x - 2 = 0 gives x = 2 x - 4 = 0 gives x = 4 There are two values for x. For each of these two values for x, we must find a corresponding value for y. We use y = 6 - x To find the y-value that corresponds to x = 2 y = 6 - 2 y = 4 So one solution is the point (x, y) = (2, 4) To find the y-value that corresponds to x = 4 y = 6 - 4 y = 2 So the other solution is the point (x, y) = (4, 2) Edwin McCravy AnlytcPhil@aol.com``` Answer by fractalier(2101)   (Show Source): You can put this solution on YOUR website!Well this one can actually be done by just looking at it: xy=8 x+y=6 and know it is 4 and 2 or 2 and 4, but solve the second one for x and substitute it into the first equation... x = 6 - y (6 - y)y = 8 6y - y^2 = 8 y^2 - 6y + 8 = 0 (y - 4)(y - 2) = 0 y = 4 or y = 2 x = 2 or x = 4