math

(Systems) how do I solve 5x+3y=2 and x+2y=6 using substition

This is what I did

X+2y=6 eq.1
5x+3y=2 eq.2
X=-3y/5

Sub(x=-3y/5) into eq.1
-3y/5 + 2y=6
7/5y=6
y=30/7

Sub(y=30/7) into eq.2
5x+3(30/7)=3
5x+90/7=3
5x=-69/7
x= -68/35


The answer I got was (-68/35, 30/7) but I know it's wrong because there were no fractions in the possible answers.

I know how to solve it with elimination but I can't figure out how to do it with substitution.

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  1. Why not take the easier equation?
    x+2y=6 ---> x = 6-2y

    now plug that into the other,
    5x+3y=2
    5(6-2y) + 3y = 2
    30 - 10y + 3y = 2
    -7y = -28
    y = 4
    then x = 6 -2(4) = -2

    see how easy it is ?

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  2. Thank u!

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  3. Your mistake happened early. You said

    5x+3y=2 eq.2
    X=-3y/5

    but really

    x = (2-3y)/5

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