SOLUTION: 2x^2 - 3xy +y^2 =14 2x - y = 7 Please help having hard time solving this one. Thank you

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 2x^2 - 3xy +y^2 =14 2x - y = 7 Please help having hard time solving this one. Thank you      Log On


   

Question 141346: 2x^2 - 3xy +y^2 =14
2x - y = 7
Please help having hard time solving this one. Thank you
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
From the second equation, y=2x-7. Plug this in for y in the first equation.

2x%5E2-3x%282x-7%29%2B%282x-7%29%5E2=14 <-- Substitution
2x%5E2-6x%5E2%2B21x%2B4x%5E2-28x%2B49=14<--- expand all terms
-7x%2B35=0 <---combine,cancel
x=5<--- solve
Now, plug this value for x in the second equation: y=2%285%29-7=3
The solution set is (5,3).
Check:
2(25)-3(5)(3)+9=50-45+9=14
2(5)-3=7