Question 141346
From the second equation, y=2x-7. Plug this in for y in the first equation.


{{{2x^2-3x(2x-7)+(2x-7)^2=14}}} <-- Substitution
{{{2x^2-6x^2+21x+4x^2-28x+49=14}}}<--- expand all terms
{{{-7x+35=0}}} <---combine,cancel
{{{x=5}}}<--- solve

Now, plug this value for x in the second equation: {{{y=2(5)-7=3}}}

The solution set is (5,3).

Check:

2(25)-3(5)(3)+9=50-45+9=14

2(5)-3=7