SOLUTION: 2x-3y-10=0 and x^2+xy+y^2+2x+y-6=0. Solve please

Question 856324: 2x-3y-10=0 and x^2+xy+y^2+2x+y-6=0. Solve please
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Solve the linear equation for x in terms of y (or the other way around if you want); substitute this into the conic section equation, and simplify. You are looking to solve a quadratic equation in ONE variable which may have two solutions, or possibly one solution. Can you do this without more help?

"No."

---Use this in the quadratic equation and again later after finding values for y.
-
The substitution:

...combine like terms and simplify ...

---- you could try to factor this, but much easier to use the general solution to a quadratic equation.
-
Discriminant is
The solution will contain an Imaginary component. The discriminant is less than zero.
! you would expect the two graphs to share not any points; no intersections.
-
-
Another try done on paper but solving first for x instead of y in the linear equation and then substituting, gave me after simplifications, ;
and the discriminant, "b^2-4*a*c", is , a value less than zero. This again means that the solution for x will contain an Imaginary component. The given conic section and the given line DO NOT INTERSECT!
RELATED QUESTIONS
3y+2x=1 and... (answered by ikleyn,Shin123)

xy+2x+3y+6/xy+2x+y+2 (answered by stanbon)

2x+y=2 xy=6... (answered by Fombitz)

Please help me solve for x and y simultaneously {{ y-2x+1 and... (answered by Alan3354)

if xy<0 and y>0 which of the following must be positive? A.x-y B.2x+3y C.x+10/y+2... (answered by Theo)

2x+Y=10 X=2... (answered by josgarithmetic)

Y-2x=-2 and x^2+y^2+2x-3y=19. Please solve it... (answered by Fombitz)

solve by substitution 1. 4x + 5y= 6 y=2x - 10 2. 4x-3y=0... (answered by MathLover1)

solve the simultaneous equatoon x^2+xy-4y^2=2.......Eq1 2x-3y=1.........eq2 find x and (answered by josgarithmetic,MathTherapy)