1. 1
Solve: $$y-x=1$$ $$y=x^2-2x-3$$
2. 2
Solve: $$y=4x-4$$ $$y=x^2+3x-4$$
3. 3
Solve: $$x-y=3$$ $$y=x^2-x-11$$
4. 4
Solve: $$3x-y=-9$$ $$y=2x^2+3x+1$$
5. 5
Solve: $$2x+y-8=0$$ $$y=3x^2+x-10$$
6. 6
Solve: $$x+y-5=0$$ $$x^2+y^2=25$$

This is not a linear-quadratic system, but the same concept applies to solving this. (the second equation is a circle)
7. 7
Solve: $$x-y-1=0$$ $$x^2+y^2=25$$
8. 8
Solve: $$x-y+3=0$$ $$x^2+y^2=29$$
9. 9
Solve: $$3x-y=0$$ $$x^2+y^2=10$$

$$e=mc^2$$