As of 2019, the New York Yankees had won the World Series more than any other team in baseball. The difference of the number of World Series championships won by the Yankees and 2 times the number of World Series championships won by the second-most-winning team, the St. Louis Cardinals, is 5. The sum of the two teams' World Series championships is 38. a. Write a system of equations to find the number of World Series championships won by the Yankees, y, and the number of World Series championships won by the Cardinals, x.

1) The system of equations are;

y - 2·x = 5

y + x = 38

2) y = 27 World Series championships

x = 11 World Series championships

Step-by-step explanation:

1) The number of World Series championships won by the Yankees = y

The second most-winning team = The St. Louis Cardinals

The number of World Series championships won by the St, Louis Cardinals = x

From the details of the number of World Series won by the Yankees and the St. Louis Cardinals we are given, we can write the following system of equations  to find the number of World Series championships won by the Yankees, 'y', and the number of World Series championships won by the Cardinals, 'x' as follows;

y - 2·x = 5...(1)

y + x = 38...(2)

2) Making 'y' the subject of both equations gives;

For equation (1)

y = 5 + 2·x

For equation (2)

y = 38 - x

Equating both 'y' values gives;

y = 5 + 2·x = 38 - x

2·x + x = 38 - 5

3·x = 33

∴ x = 33/3 = 11

The number of World Series championships won by the St, Louis Cardinals, x = 11 World Series championships

From y = 38 - x, we have;

y = 38 - x

∴ y = 38 - 11 = 27

Therefore, the number of World Series championships won by the Yankees, y = 27 World Series championships

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

5x+2x=49

7x=49

x=7. 35 apples