The solution to a system of linear equations is (negative 3, negative 3). Which system of linear equations has this point as its solution?

Question

x minus 5 y = negative 12 and 3 x + 2 y = negative 15
x minus 5 y = negative 12 and 3 x + 2 y = 15
x minus 5 y = 12 and 3 x + 2 y = negative 15
x minus 5 y = 12 and 3 x + 2 y = 15

Answer 1

To determine which system of linear equations has the solution \((-3, -3)\), we will substitute \(x = -3\) and \(y = -3\) into each of the given options and check which one holds true.

1. Option 1: \(x - 5y = -12\) and \(3x + 2y = -15\)

   Substitute \(x = -3\) and \(y = -3\):

   • First equation: \[ -3 - 5(-3) = -3 + 15 = 12 \quad \text{(not true)} \]
   • Second equation: \[ 3(-3) + 2(-3) = -9 - 6 = -15 \quad \text{(true)} \]

   Since the first equation is not satisfied, this system does not work.

2. Option 2: \(x - 5y = -12\) and \(3x + 2y = 15\)

   Substitute \(x = -3\) and \(y = -3\):

   • First equation: \[ -3 - 5(-3) = -3 + 15 = 12 \quad \text{(not true)} \]
   • Second equation: \[ 3(-3) + 2(-3) = -9 - 6 = -15 \quad \text{(not true)} \]

   This system does not work either.

3. Option 3: \(x - 5y = 12\) and \(3x + 2y = -15\)

   Substitute \(x = -3\) and \(y = -3\):

   • First equation: \[ -3 - 5(-3) = -3 + 15 = 12 \quad \text{(true)} \]
   • Second equation: \[ 3(-3) + 2(-3) = -9 - 6 = -15 \quad \text{(true)} \]

   Both equations are satisfied, so this system works.

4. Option 4: \(x - 5y = 12\) and \(3x + 2y = 15\)

   Substitute \(x = -3\) and \(y = -3\):

   • First equation: \[ -3 - 5(-3) = -3 + 15 = 12 \quad \text{(true)} \]
   • Second equation: \[ 3(-3) + 2(-3) = -9 - 6 = -15 \quad \text{(not true)} \]

   This system does not work.

Thus, the only system that has the solution \((-3, -3)\) is Option 3: \(x - 5y = 12\) and \(3x + 2y = -15\).