Question

Which equations represent the situation where the difference between twice a number, x, and a smaller number, y, is 3, and the sum of twice the number and the smaller number is -3?

a) y - 2x - 3 and y = -2x
b) y - 2x - 3 and y = -x
c) y - 2x + 3 and y = -2x - 3
d) y - 2x + 3 and y = -1/2x - 3/2

Answer 1

The correct equations that represent the given situation where the difference between twice a number, x, and a smaller number, y, is 3, and the sum of twice the number and the smaller number is -3, are y - 2x - 3 and y = -2x.

Step-by-step explanation:

The correct equations that represent the given situation are y - 2x - 3 and y = -2x, which corresponds to option (a). Let's break down the problem step by step to understand how we arrived at these equations:

1. The difference between twice a number, x, and a smaller number, y, is 3. This can be written as 2x - y = 3.
2. The sum of twice the number, x, and the smaller number, y, is -3. This can be written as 2x + y = -3.
3. Combining the two equations, we get 2x - y = 3 and 2x + y = -3.
4. Adding the two equations, we eliminate the y term and get 4x = 0.
5. Solving for x, we find that x = 0.
6. Substituting x = 0 into one of the original equations, we can solve for y and find that y = -2x.

Therefore, the correct equations are

y - 2x - 3

and

y = -2x