UK Secondary (7-11)
Number and nature of solutions to non-linear systems

## Interactive practice questions

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?

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A graph of the equations $y=2x+3$y=2x+3 and $\left(x-2\right)^2+\left(y-3\right)^2=4$(x2)2+(y3)2=4 is shown below.

How many real solutions does this system of equations have?

A graph of the equations $x^2+y^2=25$x2+y2=25 and $12x+5y-65=0$12x+5y65=0 is shown below.

How many real solutions does this system of equations have?

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

How many real solutions does this system of equations have?