Question 1:
S = {0,1}
Is Set S closed under addition?
Why or why not?

9514 1404 393

  no; 1+1=2, a number not in the set

Step-by-step explanation:

A set is closed under addition if the addition of any two members of the set results in a member of the set.

  0 + 0 = 0 . . . in the set

  0 + 1 = 1 . . . in the set

  1 + 0 = 1 . . . in the set

  1 + 1 = 2 . . . not in the set. The set is not closed under addition.

(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