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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)

The equation for the bank account balance is y=
.

5 answers

To find the equation for the bank account balance at the local bank, we will use the information given:

  • The initial deposit is $100.
  • The monthly deposit is $15.

The account balance can be expressed in a linear form, where \(y\) is the account balance and \(x\) is the number of months after the initial deposit. The formula for the bank account balance will be:

\[ y = \text{initial deposit} + (\text{monthly deposit} \times \text{number of months}) \]

Substituting in the values:

\[ y = 100 + 15x \]

So, the equation for the bank account balance is:

\[ y = 15x + 100 \]

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.
(1 point)
Responses

{x+3=2y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals negative x minus 10 end layout

{x+3=2+y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 plus y second row 5 y equals negative x minus 10 end layout

{x+3=2y5y=x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals x minus 10 end layout

{3x=2y5y=−x−10

Based on the description provided, we are looking for a system of equations that captures the two statements:

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

We can translate these statements into equations:

  1. The first statement can be expressed as: \[ x + 3 = 2y \]

  2. The second statement can be expressed as: \[ 5y = -x - 10 \]

Combining these, we have the system of equations:

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

So the correct response based on your options is:

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

Use the image to answer the question.

Two parallel lines slope upward on a coordinate plane. A dotted line passes through the plotted point left parenthesis 0 comma 0 right parenthesis. A solid line intersects the y-axis at left parenthesis 0 comma 3 right parenthesis.

Write the equations for the system of linear equations graphed.

(1 point)
The equation of the solid line is y=
, and the equation of the dotted line is y=
.

To derive the equations for the two lines based on your description, let's break down the details:

  1. Solid Line:

    • The solid line intersects the y-axis at the point (0, 3). This is the y-intercept, so the equation will have the form: \[ y = mx + b \] where \( b = 3 \) (the y-intercept).
    • You mentioned there are two parallel lines that slope upward. Therefore, the slope \( m \) will be some positive value. Let's assume the slope of the solid line is \( m \) (you would need to refer to the image to determine the exact value).
    • Thus, the equation for the solid line will be: \[ y = mx + 3 \] (Replace \( m \) with the exact value of the slope if you have it from the image.)

  2. Dotted Line:

    • The dotted line passes through the origin (0, 0), which means the y-intercept is 0. Therefore, its equation will also have the form: \[ y = mx + b \] where \( b = 0 \).
    • Again, since it is parallel to the solid line, it will have the same slope \( m \).
    • Hence, the equation for the dotted line will be: \[ y = mx \] (Replace \( m \) with the exact slope value.)

In conclusion, your equations will be:

  • The equation of the solid line is: \[ y = mx + 3 \]
  • The equation of the dotted line is: \[ y = mx \]

Make sure to replace \( m \) with the precise slope from the graph if you have that information.