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ashleysmith

How do you determine if linear equations are parallel without graphing like 2x + 2y=4 3x +y=3

  • one year ago
  • one year ago

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  1. lgbasallote
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    simplify the equations as much as possible for example 2x + 2y = 4 i can divide all terms by 2 and simplify it to x + y = 2 got that part?

    • one year ago
  2. ashleysmith
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    Yeah , after you simplify it how do you know if it's parallel or perpendicular

    • one year ago
  3. lgbasallote
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    you look at the next equation (note that it has to be simplified as much as possible too) our first equation is x + y = 2 if our second equation is also x+y = c <---c is a constant (which means it is any number)..the important thing is the x+y if the left sides of BOTH equations look EXACTLY the same then they are parallel got it?

    • one year ago
  4. ashleysmith
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    Yeah what if the slope is the same ?

    • one year ago
  5. lgbasallote
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    when the slopes are the same then they are parallel

    • one year ago
  6. lgbasallote
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    to know if it is perpendicular...simplify the equations again...then put it in the form ax + by = c so you can see it better now when the left sides of BOTH equations look the same BUT the only difference is the sign of x, then they are perpendicular

    • one year ago
  7. lgbasallote
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    would you like an example?

    • one year ago
  8. ashleysmith
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    Sure:)

    • one year ago
  9. lgbasallote
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    okay... 2x + 2y = 4 3y = 9 - 3x the first step is to simplify both equations..i divide the first equation by 2 and get x + y = 2 now i divide the second equation by 3 (since it is common to all terms) y = 3 - x now the second step is to put in the form ax + by = c the first equation is already in that form so no worries the second equation would then look like x + y = 3 now let us compare (1) x + y = 2 (2) x + y = 3 what can you say?

    • one year ago
  10. ashleysmith
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    Parallel!!

    • one year ago
  11. ashleysmith
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    Thank you so much

    • one year ago
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