4y-x=5+2y; 3x+7y=24 solve systen by using substitution

4y - x = 5 + 2y (1)
3x + 7y = 24     (2)

by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
-x + 2y = 5         (1a)

by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x  -  6y = -15   (1b)

by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
                      13y = 39
           ⇒            y = 3

by substituting y=3 into (2)
    3x + 7(3) = 24 
              3x = 24 - 21
              3x = 3
        ⇒     x = 1

∴ solution to the system is x=1 when y = 3

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