Question

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below.

x – y = 4

x + y = 18

Which two numbers did Mira pick?

(10, 8)

(18, 4)
(20, 16)
(40, 32)

Answer 1

Let

x------> the first number

y-----> the second number

Assume
`x> y`

we know that

`x-y=4` ----> equation A

`(x)/(2)+ (y)/(2)=18`

Multiply by
`2` both sides

`x+y=36`-----> equation B

Adds equation A and equation B

`x-y=4 \\x+y=36\\------- \\ x+x=4+36\\ 2x=40\\ x=20`

Find the value of y

`20-y=4`

`y=20-4=16`

therefore

the answer is the option

`(20,16)`

Answer 2

Based on the description, the system can be explained in equation form as x - y =4, an (x + y)/2 = 18. Based on these equations, we can plus in numbers from the given answers and come up with a solution where both equations are satisfied. The two numbers that satisfy both equations are (20, 16).