math

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please help, I have a test tomorrow and i don't get this.

solve by substitution
1. y = x - 3
x + y = 5

2. 5x + 2y = 0
x - 3y =0

  • math -

    if y=x-3, then you have to plug it into the equation.
    for numb 1, y=x-3 so when you plug that in it makes the equation x+y=5 turns into x+x-3=5. then you solve by making the sides equal.

    you do this by x+x-3=5
    x-3=3
    x=2

  • math -

    I'm with Zava on the idea, but I think one of us dropped a sign along the way. And I'm not at all sure it wasn't me, so I'll check at the end. Dropped signs happen all the time.

    We have:

    x + y = 5

    but we're also given what y is: y = x - 3

    So we can just replace y in the equation with (x-3)

    x + y = 5

    x + (x-3) = 5

    2x - 3 = 5

    2x = 5 + 3

    2x = 8

    x = 4

    and since y = x -3

    y = 4 - 3 = 1

    Check:

    y = x - 3
    1 = 4 - 3 - OK

    x + y = 5
    4 + 1 = 5 - OK


    The second one is a leetle trickiersince you''ll have to make one of the equations work for the substitution

    x - 3y = 0

    -> x = 3y --- that's the one we'll use!

    5x + 2y = 0

    5(3y) + 2y = 0

    17y = 0 -> y = 0.

    No that's not a mistake. The only answer is if x and y are both zero!

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