Question

Solve the system of equations. 8x−4y=−28 2x−6y=8 (1 point) Responses (−5,−3) left parenthesis negative 5 comma negative 3 right parenthesis (−2, 3) left parenthesis negative 2 comma 3 right parenthesis (−4,−1) left parenthesis negative 4 comma negative 1 right parenthesis (7, 1)

Answer 1

For renting tables, Parties ‘R Us charges, C , a $60 delivery fee and $4 per table, t . Rob’s Rentals charges, C , a $40 delivery fee and $6 per table, t . Write the pair of linear equations that model this situation.(1 point) Responses Parties ‘R Us: C=60t+6 ; Rob’s Rentals: C=40t+4 Parties ‘R Us: upper C equals 60 t plus 6 ; Rob’s Rentals: upper C equals 40 t plus 4 Parties ‘R Us: C=60t+4 ; Rob’s Rentals: C=40t+6 Parties ‘R Us: upper C equals 60 t plus 4 ; Rob’s Rentals: upper C equals 40 t plus 6 Parties ‘R Us: C=4t+40 ; Rob’s Rentals: C=6t+60 Parties ‘R Us: upper C equals 4 t plus 40 ; Rob’s Rentals: upper C equals 6 t plus 60 Parties ‘R Us: C=4t+60 ; Rob’s Rentals: C=6t+40

Answer 2

To solve the system of equations:

1. **First equation:**
\(8x - 4y = -28\)
We can simplify this by dividing the entire equation by 4:
\[ 2x - y = -7 \quad \text{(Equation 1)} \]

2. **Second equation:**
\(2x - 6y = 8\)
We can simplify this by dividing the entire equation by 2:
\[ x - 3y = 4 \quad \text{(Equation 2)} \]

Now we have a simpler system of equations:
1. \(2x - y = -7\)
2. \(x - 3y = 4\)

Next, we can solve this system using substitution or elimination. Let's use substitution. From Equation 1, we can express \(y\) in terms of \(x\):

\[ y = 2x + 7 \]

Now, substitute \(y\) into Equation 2:

\[ x - 3(2x + 7) = 4 \]

Distributing the \(-3\) gives:

\[ x - 6x - 21 = 4 \]

Combine like terms:

\[ -5x - 21 = 4 \]

Add 21 to both sides:

\[ -5x = 25 \]

Now, divide by \(-5\):

\[ x = -5 \]

Now that we have \(x\), we can find \(y\) using the expression for \(y\):

\[ y = 2(-5) + 7 \]
\[ y = -10 + 7 \]
\[ y = -3 \]

Thus, the solution to the system of equations is:

\((-5, -3)\)

Therefore, the answer is:
\((-5, -3)\)

Answer 3

To model the costs for renting tables from Parties 'R Us and Rob's Rentals, we will write equations based on the provided delivery fees and costs per table.

1. **Parties 'R Us:**
- Charges a **$60 delivery fee**.
- Charges **$4 per table**.
Therefore, the equation for Parties 'R Us can be written as:
\[
C = 60 + 4t
\]

2. **Rob's Rentals:**
- Charges a **$40 delivery fee**.
- Charges **$6 per table**.
Therefore, the equation for Rob's Rentals can be written as:
\[
C = 40 + 6t
\]

Putting these two equations together, we have the following pair of linear equations:

- Parties 'R Us: \( C = 60 + 4t \)
- Rob's Rentals: \( C = 40 + 6t \)

Hence, the correct response that represents the situation is:

**Parties ‘R Us: \( C = 60 + 4t \); Rob’s Rentals: \( C = 40 + 6t \)**

(Note: There may have been a small misalignment from common equation format; if check your provided options closely, there should be alignment with correct delivery fee and table rate placements.)