# SOLUTION: Solve the system by substitution. x + 2y = 11 –2x + 4y = –6 Answer: x = y =

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 Question 81713: Solve the system by substitution. x + 2y = 11 –2x + 4y = –6 Answer: x = y = Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!Given: . + x + 2y = 11 –2x + 4y = –6 . Solve the top equation for x. Do this by subtracting 2y from both sides to make the top equation become: . x = 11 - 2y . Then go to the bottom equation and substitute 11 - 2y for x. When you do that substitution, the bottom equation becomes: . -2(11 - 2y) + 4y = -6 . Do the distributed multiplication on the left side by multiplying -2 times both of the terms inside the parentheses. Doing that multiplication results in: . -22 + 4y + 4y = -6 . Get rid of the -22 on the left side by adding 22 to both sides. This makes the equation: . +4y + 4y = 16 . Add the two terms on the left side to get: . 8y = 16 . Solve for y by dividing both sides by 8, the multiplier of y. This division results in: . y = 16/8 = 2 . Now that we know that y is 2, we can return to one of the two original equations, substitute 2 for y in that equation and solve for x. Let's return to the top equation: . x + 2y = 11 . Substitute 2 for y and get: . x + 2(2) = 11 . Multiply out: . x + 4 = 11 . Get rid of the 4 on the left side by subtracting 4 from both sides to get: . x = 11 - 4 = 7 . So the answers to this problem are x = 7 and y = 2. . Hope this helps you to understand the problem and how to work out a solution by substitution.