Question

the larger of two numbers exceeds twice the smaller by one. three times the smaller exceeds the larger by six. if y is the larger number, which of the following systems of equations represents the word problem? 1.y=2x+1 and 3x+6=y 2. y=2x+1 and y+6=3x 3.y=2(x+1) and y+6=3x​

Answer 1

The larger of two numbers exceeds twice the smaller by one. The system of equations are y = 2x + 1 and y + 6 = 3x. So option 2 is correct

Solution:

Given, y is the larger number and x be the smaller number.

We have to find which of the given systems of equations represents the word problem?  

Now, the larger of two numbers exceeds twice the smaller by one.  

Then, y – (2 × x) = 1 ⇒ y – 2x = 1 ⇒ y = 2x + 1

And, three times the smaller exceeds the larger by six  

Then, 3 × x – y = 6 ⇒ 3x – y = 6 ⇒ y + 6 = 3x

Hence, the system of equations are y = 2x + 1 and y + 6 = 3x. so option 2 is correct.