SOLUTION: If x + y = 5 and x^2 + 3xy + 2y^2 = 40, find the value of (2x + 4y).
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Question 256779: If x + y = 5 and x^2 + 3xy + 2y^2 = 40, find the value of (2x + 4y).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 2 equations.
they are
x + y = 5
x^2 + 3xy + 2y^2 = 40
solve for y in the first equation to get y = 5-x
substitute for y in the second equation to get:
x^2 + 3x(5-x) + 2(5-x)^2 = 40
simplify to get:
x^2 + 15x - 3x^2 + 2 * (25 - 10x + x^2) = 40
simplify further to get:
x^2 + 15x - 3x^2 + 50 - 20x + 2x^2 = 40
combine like terms to get:
-5x + 50 = 40
subtract 50 from both sides of eqution to get:
-5x = 40 - 50 = -10
multiply both sides by -1 to get:
5x = 10
divide both sides by 5 to get:
x = 2
substitute in first equation to get:
x + y = 5 becomes 2 + y = 5 becomes y = 3
you have x = 2 and y = 3
2x + 4y = 2*2 + 4*3 = 4 + 12 = 16
your answer is (2x + 4y) = 16.
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