Substitution type simultaneous equations

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Question from Kayla, a student:

I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^2-3x+4 and 3x-2y=1
I have rearranged 3x-2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you.

OMG Kayla that's ugly. I rearranged $3x-2y=1$ to get $ y = \large \frac{3x - 1}{2}$ and than substituted into $y = x^2-3x+4.$ Try that and see if you get the correct answer.

Penny

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