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Solve using elimination.\newline−x−7y=−13-x - 7y = -13\newline4x−7y=174x - 7y = 17\newline(_____, _____)

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Q. Solve using elimination.\newline−x−7y=−13-x - 7y = -13\newline4x−7y=174x - 7y = 17\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline−x−7y=−13-x - 7y = -13\newline4x−7y=174x - 7y = 17
  2. Add Equations: Add the two equations together to eliminate the yy variable.\newline(−x−7y)+(4x−7y)=(−13)+(17)(-x - 7y) + (4x - 7y) = (-13) + (17)\newlineThis simplifies to:\newline−x+4x=4x−x=3x-x + 4x = 4x - x = 3x\newline−7y−7y=−14y-7y - 7y = -14y (This term will be eliminated)\newline−13+17=4-13 + 17 = 4\newlineSo, we get:\newline3x=43x = 4
  3. Solve for x: Solve for x.\newline3x=43x = 4\newlineDivide both sides by 33 to isolate xx:\newlinex=43x = \frac{4}{3}
  4. Substitute xx: Substitute x=43x = \frac{4}{3} back into one of the original equations to solve for yy. We'll use the first equation:\newline–x−7y=–13–x − 7y = –13\newlineSubstitute xx:\newline–(43)−7y=–13–\left(\frac{4}{3}\right) − 7y = –13
  5. Solve for y: Solve for y.\newlineMultiply both sides of the equation by 33 to clear the fraction:\newline−3∗(43)−3∗7y=−3∗13-3*(\frac{4}{3}) - 3*7y = -3*13\newlineThis simplifies to:\newline−4−21y=−39-4 - 21y = -39\newlineNow, add 44 to both sides:\newline−21y=−39+4-21y = -39 + 4\newline−21y=−35-21y = -35\newlineNow, divide both sides by −21-21 to solve for y:\newliney=−35−21y = \frac{-35}{-21}\newliney=3521y = \frac{35}{21}\newliney=53y = \frac{5}{3}

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