simultaneous equation one linear and one quadratic

Question

   2x-3y-10=0 and x^2+xy+y^2+2x+y-6=0               please explain in detail because it is really killing me,thanks 

Answer 1

Joseph,

 

Here's a target: http://www.wyzant.com/resources/files/266492/rotated_ellipse_and_line.

 

Try to find exact values for solution points.

Answer 2

     One way to solve this is first solve the linear equation for y in terms of x and then substitute that for y in the quadratic and simplify you will wind up with a quadratic in x which you should be able to solve (find the roots).  Then substitute each root in the liner equation and calculate the corresponding y's. Lastly check your results by subbing each x,y pair in the quadratic to make sure they solve that equation. Lots of algebra but straight forward.

 

Jim