To create a true equivalent system from the equations provided in System A and System B, we need to find an equation that maintains the same solutions as the original equations.
The equations in System B, \(x + y = 11\), can be manipulated.
If we multiply both sides of the equation by 2, we would have: \[ 2(x + y) = 2(11) \] This simplifies to: \[ 2x + 2y = 22 \] Now, to check which option matches or creates an equivalent system, let’s look at the options:
- \(2y = 12\) – This simplifies to \(y = 6\), not equivalent to the original.
- \(2x + 2y = 12\) – This is not equivalent to the original \(x + y = 11\).
- \(-x - y = -1\) – This can also be transformed by multiplying by -1 to get \(x + y = 1\), which is not equivalent to \(x + y = 11\).
- \(-2x - 2y = -22\) – This is equivalent to dividing by -2, which gives us \(x + y = 11\).
Therefore, the equation that creates a true equivalent system is: \[ -2x - 2y = -22 \]
Thus, the correct answer is:
\(-2x - 2y = -22\).