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what is the answer to this in solving systems by elimination form {2x-3y=9 {-5x-3y=30

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Answer:  

Step-by-step explanation:

2x - 3y = 9

    -5x - 3y = 30

For simplicity, let's eliminate the y variable in this system by multiplying the second equation by -1:

            -1·(-5x - 3y = 30)    

  ==>   -1·-5x  -  -1·3y  =  -1·30    

  ==>   5x + 3y = -30

Add this equation to the first original equation:

       2x   -  3y  = 9

  +   5x  +  3y  =  -30  

  __________________

  2x + 5x - 3y + 3y = 9 + -30     ==>     7x  +  0y  =  -21     ==>     7x  =  -21

    7x  =  -21

    7x/7  =  -21/7     ==>     x = -3

Plug this value for x into either of the original equations from the system (I will use the first equation) to solve for y:

    2x - 3y = 9

    2·(-3)  -  3y  =  9

    -6  -  3y  =  9

Add 6 to both sides of the equation:

 -6  +  6  -  3y  =  9  +  6

-3y  =  15

Divide both sides of the equation by -3:

   -/-3  =  15/-3

     y = -5

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