You most use a system of two equations in two variables. I need help please.

## The difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. find the numbers.

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# 2 Answers

Hi Alexander;

x...smaller number

x+16...larger number

5x=[2(x+16)]-8

Distribute the 2...

5x=2x+32-8

Combine like terms...

5x=2x+24

Subtract 2x from both sides...

5x-2x=2x-2x+24

3x=24

Divide both sides by 3...

(3x)/3=24/3

**x=8**

**x+16=24**

Let's check our work...

(5)(8)=[(2)(24)]-8

40=48-8

40=40

let x be the larger number

let y be the smaller number

x-y=16

5y=2x-8

x-y=16, x=y+16

substitute y+16 for x in the equation 5y=2x-8

5y=2(y+16)-8

5y=2y+32-8

5y=2y+24

5y-2y=2y-2y+24

3y=24

y=8

x-8=16

x=24

the larger number is 24 and the smaller number is 8

check:5*8=40 and 2*24=48

40 is 8 less than 48