Systems of Linear Equations Online Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
8 of 138 of 13 Items

Question
(4,−3)
is the correct solution to which system?(1 point)
Responses

7x−9y=55

3x+ 9y=−15
7 x minus 9 y equals 55 3 x plus 9 y equals negative 15

7x−9y=55

3x− 9y=−15
7 x minus 9 y equals 55 3 x minus 9 y equals negative 15

7x+9y=55

3x+ 9y=−15
7 x plus 9 y equals 55 3 x plus 9 y equals negative 15

7x+9y=55

3x−9y=−15

Answer 1

To determine which system of equations has (4, -3) as its solution, we need to substitute x = 4 and y = -3 into each option and check if both equations yield true statements.

1. For the first system:

   • Equation 1: \(7x - 9y = 55\) \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(True)} \]
   • Equation 2: \(3x + 9y = -15\) \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(True)} \]
   • This system is valid.

2. For the second system:

   • Equation 1: \(7x - 9y = 55\) \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(True)} \]
   • Equation 2: \(3x - 9y = -15\) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(False)} \]
   • This system is not valid.

3. For the third system:

   • Equation 1: \(7x + 9y = 55\) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(False)} \]
   • Equation 2: \(3x + 9y = -15\) \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(True)} \]
   • This system is not valid.

4. For the fourth system:

   • Equation 1: \(7x + 9y = 55\) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(False)} \]
   • Equation 2: \(3x - 9y = -15\) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(False)} \]
   • This system is not valid.

The valid system of equations for which (4, -3) is a solution is:

• 7x - 9y = 55
• 3x + 9y = -15.