To find an equation that creates a true equivalent system with the given equations from System A and System B, we first need to examine the equations closely.
From System A:
- \(-x + y = 1\)
From System B:
- \(x + y = 11\)
Now let's solve the equation from System A for \(y\): \[ y = x + 1 \]
Next, we substitute \(y\) into the equation from System B: \[ x + (x + 1) = 11 \] \[ 2x + 1 = 11 \] \[ 2x = 10 \] \[ x = 5 \]
Using the value of \(x\), we can find \(y\): \[ y = 5 + 1 = 6 \]
Thus, the solution of the system is \(x = 5\) and \(y = 6\).
Now, let's check the proposed equations for equivalence:
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\(-2x - 2y = -22\): This equation can be simplified by dividing through by -2, resulting in \(x + y = 11\), which is equivalent to an equation in System B.
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\(2x + 2y = 12\): Dividing this by 2 gives \(x + y = 6\), which is not equivalent to the original systems.
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\(-x - y = -1\): This rearranges to \(x + y = 1\), which is again not equivalent to the original systems.
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\(2y = 12\): This simplifies to \(y = 6\). This does not account for the value of \(x\) and does not show an equivalent relationship.
The only equation that creates a true equivalent system is: (-2x - 2y = -22.
So the correct response is:
−2x−2y=−22 (negative 2 x minus 2 y equals negative 22).