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

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 2

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 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.)