Question

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 time

the smaller number. Which equations represent the situation?
O 2x-y--6 and 3x-y--5
O 2x-y--3 and 3x-y--5
O 2x-y--6 and x-3y-5
O 2x-y--3 and x-3y-5
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Answer 1

So the smaller number is x = 1 and the larger number is y = 8.

Explanation:

substitute y = 3x + 5 into the first equation and solve for x.

y = 2(x + 3) 3x + 5 = 2(x + 3) Expand the parentheses 3x + 5 = 2x + 6 Subtract 2x from both sides x + 5 = 6 Subtract 5 from both sides x = 1

Now we can plug x = 1 into either equation to find y.

y = 2(x + 3) y = 2(1 + 3) y = 2(4) y = 8