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4 November, 05:08

System of equations (substitution methods) can someone solve these problems x=3y-5; x+y=3 y=x; 3x+3y=18 y=3x+4; 5x-y=0

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  1. 4 November, 05:38
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    (1,2)

    (3,3)

    (-1/2, 11/2)

    Step-by-step explanation:

    A system of equations is 2 or more equations for which the same x, y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. Substitution can be used by substituting the value of one variable into the equation.

    Pair x=3y-5 and x+y=3

    Because x=3y-5, we can substitute 3y-5 into x in x+y=3

    x+y=3

    (3y-5) + y=3

    3y-5+y=3

    4y-5=3

    4y-5+5=3+5

    4y=8

    y=2

    We now substitute y=2 into x=3y-5.

    x=3y-5

    x=3 (2) - 5

    x=6-5

    x=1

    Pair y=x and 3x+3y=18

    Because y=x, we can substitute x into y in 3x+3y=18

    3x+3y=18

    3x+3x=18

    6x=18

    x=3

    We now substitute x=3 into y=x.

    y=3.

    Pair y=-3x+4 and 5x-y=0

    Because y=-3x+4, we can substitute - 3x+4 into y in 5x-y=0

    5x-y=0

    5x - (-3x+4) = 0

    5x+3x+4=0

    8x+4=0

    8x=-4

    x=-1/2

    We now substitute x=-1/2 into y=-3x+4

    y=-3x+4

    y=-3 (-1/2) + 4

    y=3/2+4

    y=11/2
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