A graph of the equations $y=x+5$y=x+5 and $x^2+y^2=25$x2+y2=25 is shown below.

How many real solutions does this system of equations have?

A graph of the equations $y=2x+3$y=2x+3 and $\left(x-2\right)^2+\left(y-3\right)^2=4$(x−2)2+(y−3)2=4 is shown below.

A graph of the equations $x^2+y^2=25$x2+y2=25 and $12x+5y-65=0$12x+5y−65=0 is shown below.

A graph of the equations $y=2x^2+4x+2$y=2x2+4x+2 and $y=6-x^2$y=6−x2 is shown below.