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Find the intersection of the lines represented by\newliney=−5x−5y=-5x-5\newlineand\newliney=3x−13y=3x-13.

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Identify direct variation and inverse variationright chevron icon

Full solution

Q. Find the intersection of the lines represented by\newliney=−5x−5y=-5x-5\newlineand\newliney=3x−13y=3x-13.
  1. Set Equations Equal: Set the two equations equal to each other to find the xx-coordinate of the intersection point.\newlineSince both equations equal yy, we can set them equal to each other: −5x−5=3x−13-5x - 5 = 3x - 13.
  2. Solve for x: Solve for x.\newlineAdd 5x5x to both sides to get: −5=8x−13-5 = 8x - 13.\newlineThen add 1313 to both sides to get: 8=8x8 = 8x.\newlineFinally, divide both sides by 88 to get: x=1x = 1.
  3. Substitute and Solve: Substitute the value of xx back into one of the original equations to find the yy-coordinate of the intersection point.\newlineUsing the first equation y=−5x−5y = -5x - 5, substitute x=1x = 1: y=−5(1)−5=−5−5=−10y = -5(1) - 5 = -5 - 5 = -10.
  4. Write Ordered Pair: Write the intersection point as an ordered pair.\newlineThe intersection point is (x,y)=(1,−10)(x, y) = (1, -10).

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