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 1/2x + 1/2 y = 18 which two numbers did mira pick?

Well, we know that:

1/2(x) + 1/2(y) = 18

2( 1/2(x) + 1/2(y) ) = 2( 18 )

x + y = 36

and

x - y = 4

if we add y to both sides of x - y = 4, we get x = 4 + y. We can substitute that into our first equation.

4 + y + y = 36

subtract 4 from both sides and add like terms: 

2y = 32

Divide both sides by 2: 

y = 16

Substitute this into our second equation: 

x - 16 = 4

Add 16 to both sides: 

x = 20

We can check this by Substituting x with 20 and y with 16: 

20 + 16 = 36

It checks out!

x = 20

y = 16