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Which ordered pair is a solution of the equation? 2x+4y=6x-y Choose 1 answer: (A) Only (4,5) (B) Only(5,4) (c) Both (4,5) and (5,4) (D) Neither

Which ordered pair is a solution of the equation?\newline2x+4y=6x−y 2 x+4 y=6 x-y \newlineChoose 11 answer:\newline(A) Only (4,5) (4,5) \newline(B) Only (5,4) (5,4) \newline(C) Both (4,5) (4,5) and (5,4) (5,4) \newline(D) Neither

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Q. Which ordered pair is a solution of the equation?\newline2x+4y=6x−y 2 x+4 y=6 x-y \newlineChoose 11 answer:\newline(A) Only (4,5) (4,5) \newline(B) Only (5,4) (5,4) \newline(C) Both (4,5) (4,5) and (5,4) (5,4) \newline(D) Neither
  1. Simplify the equation: Simplify the equation to find the relationship between x and y.\newlineWe start by moving all terms involving x to one side and all terms involving y to the other side of the equation.\newline2x+4y=6x−y2x + 4y = 6x - y\newlineSubtract 2x2x from both sides:\newline4y=4x−y4y = 4x - y\newlineAdd yy to both sides:\newline4y+y=4x4y + y = 4x\newlineCombine like terms:\newline5y=4x5y = 4x\newlineNow, divide both sides by 55 to solve for y:\newliney=45xy = \frac{4}{5}x
  2. Move terms involving x and y: Test the ordered pair (4,5)(4,5) to see if it satisfies the equation y=(45)xy = \left(\frac{4}{5}\right)x.\newlineSubstitute x=4x = 4 and y=5y = 5 into the equation:\newline5=(45)(4)5 = \left(\frac{4}{5}\right)(4)\newlineCalculate the right side:\newline5=(165)5 = \left(\frac{16}{5}\right)\newlineCheck if the left side equals the right side:\newline5≠(165)5 \neq \left(\frac{16}{5}\right)\newlineThe ordered pair (4,5)(4,5) does not satisfy the equation.
  3. Subtract 2x2x from both sides: Test the ordered pair (5,4)(5,4) to see if it satisfies the equation y=(45)xy = \left(\frac{4}{5}\right)x.\newlineSubstitute x=5x = 5 and y=4y = 4 into the equation:\newline4=(45)(5)4 = \left(\frac{4}{5}\right)(5)\newlineCalculate the right side:\newline4=(205)4 = \left(\frac{20}{5}\right)\newlineSimplify the fraction:\newline4=44 = 4\newlineCheck if the left side equals the right side:\newline4=44 = 4\newlineThe ordered pair (5,4)(5,4) satisfies the equation.

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