Which system of equations is indicated by this description?

Question

x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.

Answer 1

To translate the given description into a system of equations, we can break it down into two parts:

1. "x increased by 3 is equal to the product of 2 and y" can be expressed as: \[ x + 3 = 2y \]

2. "5 times y is equal to negative x minus 10" can be expressed as: \[ 5y = -x - 10 \]

Putting these two equations together, we have the system of equations:

\[ \begin{cases} x + 3 = 2y \ 5y = -x - 10 \end{cases} \]

This is the system of equations that corresponds to the description provided.

Answer 2

A local bank recommends opening a savings account with a $100 initial deposit and a $15 monthly deposit. A local credit union recommends opening a savings account with a $50 initial deposit and a $20 monthly deposit. A system of equations is written to find the month at which the two accounts have the same balance. If x represents the number of months after the initial deposit and y represents the account balance in dollars, the equation for the credit union account balance is y = 20x + 50. What is the equation for the bank account balance?(1 point)

Answer 3

To write the equation for the bank account balance, we will consider both the initial deposit and the monthly deposits.

1. The bank account has an initial deposit of $100.
2. It has a monthly deposit of $15.

Let \( x \) represent the number of months after the initial deposit and \( y \) represent the account balance in dollars.

The equation for the bank account balance can be written as follows:

\[ y = 15x + 100 \]

So, the equation for the bank account balance is \( y = 15x + 100 \).