`x - 2y = 1, y = sqrt(x - 1)` Solve the system graphically or algebraically. Explain your choice of method.

Let's solve this system of equations algebraically. When possible, this method gives exact results and requires no drawing.

From the second equation `xgt=1` and `ygt=0.` With these cautions we can square both sides and obtain

`y^2=x-1,` or

`x=y^2+1.`

Substitute this into the first equation and obtain

`y^2+1-2y=1,` or

`y^2-2y=0.`

So y=0 or y=2, both >=0. The corresponding x's are 1 and 5, both >=1.

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