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.
Simplify the expression in the second set of parentheses
Square the two binomials to remove the parentheses
Combine like terms.
Subtract 16 from both sides to get a 0 on the other before we use the quadratic formula.
It will be easier if we divide both sides by 2 before we use the quadratic formula.
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
The graph looks like