1. Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation?

2.

1) ok so X is smaller than Y

2Y + X = 5

5X - Y = 3

we need the equations to equal Y for simplicity

y = (5-x) / 2

Y = 5x - 3

now equate the equations to each other

(5-x) / 2 = 5x - 3

*multiply 2 to both sides

5-x = 10x - 6

*solve for x

11 = 11X

X = 1

**plug X back into any of the original equations

Y = 5 (1) - 3

y = 2

* * x = 1 and y = 2

2) ok so now the larger number x

y = x-3

y = (x+9) / 3

**same steps as before

x-3 = (x+9) / 3

*multiply 3 to both sides

3x-9 = x + 9

2x=18

x=9

plug back into original equation

y = (9) - 3

y = 6

so x=9 and y=6