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Which ordered pair is a solution of the equation?

3x+3y=-x+5y
Choose 1 answer:
(A) 
Only(1,2)
(B) Only 
(2,4)
(c) Both 
(1,2) and 
(2,4)
(D) Neither

Which ordered pair is a solution of the equation?\newline3x+3y=x+5y 3 x+3 y=-x+5 y \newlineChoose 11 answer:\newline(A) Only (1,2) (1,2) \newline(B) Only (2,4) (2,4) \newline(C) Both (1,2) (1,2) and (2,4) (2,4) \newline(D) Neither

Full solution

Q. Which ordered pair is a solution of the equation?\newline3x+3y=x+5y 3 x+3 y=-x+5 y \newlineChoose 11 answer:\newline(A) Only (1,2) (1,2) \newline(B) Only (2,4) (2,4) \newline(C) Both (1,2) (1,2) and (2,4) (2,4) \newline(D) Neither
  1. Combine like terms: Simplify the equation by combining like terms.\newlineWe need to get all the xx terms on one side and all the yy terms on the other side.\newline3x+3y=x+5y3x + 3y = -x + 5y\newlineAdd xx to both sides:\newline3x+x+3y=5y3x + x + 3y = 5y\newline4x+3y=5y4x + 3y = 5y\newlineNow, subtract 3y3y from both sides:\newline4x=5y3y4x = 5y - 3y\newline4x=2y4x = 2y
  2. Isolate xx and yy terms: Solve for yy in terms of xx.\newlineTo find the relationship between xx and yy, we divide both sides by 22:\newline4x2=2y2\frac{4x}{2} = \frac{2y}{2}\newline2x=y2x = y
  3. Solve for y in terms of x: Check the ordered pairs to see if they satisfy the equation 2x=y2x = y.\newlineFor (A) (1,2)(1,2):\newlineSubstitute x=1x = 1 and y=2y = 2 into the equation:\newline2(1)=22(1) = 2\newline2=22 = 2\newlineThis is true, so (1,2)(1,2) is a solution.
  4. Check solution (1,2)(1,2): Check the ordered pair (B) (2,4)(2,4).\newlineSubstitute x=2x = 2 and y=4y = 4 into the equation:\newline2(2)=42(2) = 4\newline4=44 = 4\newlineThis is also true, so (2,4)(2,4) is a solution.
  5. Check solution 2,42,4: Determine the final answer based on the solutions found in steps 33 and 44.\newlineSince both ordered pairs 1,21,2 and 2,42,4 satisfy the equation 2x=y2x = y, the correct answer is (C) Both 1,21,2 and 2,42,4.

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