The point (6, n) lies on the circle whose equation is (x − 1)2 + (y − 3)2 = 74. Find the values of n.
The values of n are .

n = - 4, n = 10

Step-by-step explanation:

Since the point (6, n) lies on the circle then the coordinates of the point make the equation true.

Substitute x = 6 and y = n into the equation

(6 - 1)² + (n - 3)² = 74, that is, expanding using FOIL

5² + n² - 6n + 9 = 74 ← simplifying

34 + n² - 6n = 74 ( subtract 74 from both sides and rearrange )

n² - 6n - 40 = 0 ← in standard form

(n - 10)(n + 4) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 4 = 0 ⇒ n = - 4

The values of n are - 4 and 10

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation:

compare