5. Find the points where the line whose equation is y = x - 1 meets the circle whose equation is (x - 2)2 + (y -1)2 = 16. Draw the graphs.

This system of equations is also set up for the substitution method. Substitute the formula which is equal to y in the linear function for y in the equation of the circle.

(x - 2)2 + ((x - 1) -1)2 = 16

Simplify the expression in the second set of parentheses

(x - 2)2 + (x - 2)2 = 16

Square the two binomials to remove the parentheses

x 2 - 4x + 4 + x 2 - 4x + 4 = 16

Combine like terms.

2x 2 - 8x + 8 = 16

Subtract 16 from both sides to get a 0 on the other before we use the quadratic formula.

2x 2 - 8x - 8 = 0

It will be easier if we divide both sides by 2 before we use the quadratic formula.

x 2 - 4x - 4 = 0

When we use the quadratic formula we get

32 = 16.2, and the square root of 16 is 4, so this simplifies to

We can divide the 2 in the bottom into both of the terms on top to simplify it down to

since y = x - 1, we get

If we approximate the square root of 2 with 1.414, twice the square root of 2 will be approximately 2.828. We then get our two points of intersection to be approximately

(4.828, 3.828) and (-0.828, -1.828)

The graph looks like