How will I get the point of intersection?

Question

I'm confuse on how will I get the point of intersection of these two equations: $x^2+y^2+5x+y-26=0$ and $x^2+y^2+2x-y-15=0$

I tried using the elimination method but I can't get it.

Answer 1

Hint: Subtract both the equations. You get a linear equation as follows:

$$3x+2y-11=0$$ $$y=\frac{11-3x}{2}$$ Now substitute $y$ in terms of $x$ in any of the given equations.

Answer 2

You have the equations of two circles.

If you subtract one from the other you get something like $3x+2y-11=0$ which is the line between the two points of intersection. Make $y$ (or $x$) the subject of this equation, substitute into one of the circle equations, solve the quadratic and continue as usual to answer the question.