Assume that n^2 is divisible by 3. Does it follow that n is divisible by 3

Hello,

We can work in three different cases which cover all the possibilities for n

Case 1 - We can find k such that n = 3k-1

Case 2 - We can find k such that n = 3k

Case 3 - We can find k such that n = 3k+1

So, the only case where is divisible by 3 is actually when n is divisible by 3, so if   is divisible by 3 , n is divisible by 3

Thanks

i dont get it. where are the "descriptions"?

(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