Amodern deck of cards contains fifty-two cards (thirteen in each of four suits). the four suits are hearts, diamonds, clubs, and spades. hearts and diamonds are red, and clubs and spades are black. each suit consists of cards labeled 2 through 10, followed by jack, queen, king, and ace. face cards are the jack, queen, and king; and picture cards are the jack, queen, king, and ace.
determine how many cards, in an ordinary deck of fifty-two, fit the description.
face cards and spades
determine how many cards, in an ordinary deck of fifty-two, fit the description.

Face cards and spades = 13 spades (including face cards) + 3 heart face cards + 3 diamond face cards + 3 club face cards = 22 cards

Answer = 22 cards

Spade face cards = 3 (spade king, spade queen, spade jack)

(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