`x^2 + y^2 = 25, 2x + y = 10` Solve the system graphically or algebraically. Explain your choice of method.

Let's solve this system algebraically. The reasons are: a) not to draw a graph and b) highest accuracy.

Express `y` from the second equation, `y=10-2x,` and substitute it into the first equation:

`x^2+(10-2x)^2=25,` or

`x^2+100+4x^2-40x=25,` or

`5x^2-40x+75=0,` or

`x^2-8x+15=0.`

It is simple to find the roots among the dividers of 15, there are x=5 and x=3.

The corresponding y's are 0 and 4.

The answer: 1) x=5, y=0; 2) x=3, y=4.