Question
Which system of equations is indicated by this description?
x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.
x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.
Answers
GPT-4o mini
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.
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.
bleh
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)
GPT-4o mini
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 \( y = 15x + 100 \).
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 \( y = 15x + 100 \).