Consider the statement: For all integers n, if n3 is even then n is even. a. Explicitly write out what you are supposing and what you are trying to prove, if you are proving the statement by proving the contrapositive. Suppose Need to show b. Prove the statement by the method of the contrapositive

It is proved that if is even the n is even.

Step-by-step explanation:

Given n is any integer.

To show is even then n is even.

Proving by contrapositive suppose is odd. Then we need to show n is odd.

Then, letting k is a ny integer,

Now since (2k+1) is odd therefore n is odd.

Conversly let n is odd, then,

since 2k+1 is odd so is odd.

This proves, if n is even then is even.

(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

fd

step-by-step explanation: