The sum of A and B is 171 and their difference is 35. What are the numbers?

103 and 68

Step-by-step explanation:

Given

A + B = 171

A - B = 35

Add the two expressions to eliminate B.

B + (-B) = B - B = 0

We have

2A = 206

Divide both sides by 2 to isolate A

2A/2 = 206/2

A = 103

Now substitute 103 for A in either expression to get B

Using the first expression , we have

A + B = 171

103 + B = 171

Subtract 103 from both sides

103 - 103 + B = 171 - 103

B = 68

The numbers are 103 and 68

Check

103 + 68 = 171

103 - 68 = 35

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: