Question

Use the table to answer question. System A: -x + y = x + y = 11 System B: x + y = 11 ?. Which of the following shows the equation that creates a true equivalent system?

1. 2y = 12
2. 2x + 2y = 12
3. -x - y = -1
4. -2x - 2y = -22

Answer 1

To determine an equivalent system of equations for System A and System B, we first need to clarify and examine the given equations.

From the information,
System A:
1. \(-x + y = 11\)
2. \(x + y = 11\)

System B:
1. \(x + y = 11\)

An equivalent system means that we need to manipulate the original equations while keeping the solutions the same. We can do this through algebraic transformations.

Let's analyze the options given:

1. **\(2y = 12\)**: This simplifies to \(y = 6\). This does not relate to the original equations as it is not derived from them.

2. **\(2x + 2y = 12\)**: This can be divided by 2 to yield \(x + y = 6\). This is not equivalent to \(x + y = 11\).

3. **\(-x - y = -1\)**: We can rewrite this as \(x + y = 1\) by multiplying the entire equation by -1. This is also not equivalent to the original equations.

4. **\(-2x - 2y = -22\)**: Dividing through by -2 gives \(x + y = 11\), which is indeed equivalent to the original equation \(x + y = 11\).

Thus, the correct option that creates a true equivalent system is:

**4. -2x - 2y = -22**.