Question

Systems of Linear Equations Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
10 of 1510 of 15 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 minus 9 y equals negative 15

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 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 the solution \((4, -3)\), we will substitute \(x = 4\) and \(y = -3\) into each equation of the systems provided.

1. **System 1**:
- \(7x - 9y = 55\)
- Substitute: \(7(4) - 9(-3) = 28 + 27 = 55\) (True)
- \(3x - 9y = -15\)
- Substitute: \(3(4) - 9(-3) = 12 + 27 = 39\) (False)

2. **System 2**:
- \(7x - 9y = 55\)
- Substitute: \(7(4) - 9(-3) = 28 + 27 = 55\) (True)
- \(3x + 9y = -15\)
- Substitute: \(3(4) + 9(-3) = 12 - 27 = -15\) (True)

3. **System 3**:
- \(7x + 9y = 55\)
- Substitute: \(7(4) + 9(-3) = 28 - 27 = 1\) (False)
- \(3x + 9y = -15\)
- Substitute: \(3(4) + 9(-3) = 12 - 27 = -15\) (True)

4. **System 4**:
- \(7x + 9y = 55\)
- Substitute: \(7(4) + 9(-3) = 28 - 27 = 1\) (False)
- \(3x - 9y = -15\)
- Substitute: \(3(4) - 9(-3) = 12 + 27 = 39\) (False)

The only system of equations that has the solution \((4, -3)\) is the second system:
**\(7x - 9y = 55\) and \(3x + 9y = -15\)**.