To solve the system of equations given by \( x + y = 2 \) and \( y = -x - 6 \), you can use substitution or elimination. Here, I'll use substitution:
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From the first equation, express \( y \) in terms of \( x \): \[ y = 2 - x \]
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Substitute this expression for \( y \) into the second equation: \[ 2 - x = -x - 6 \]
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Now, solve for \( x \): \[ 2 - x = -x - 6 \] Add \( x \) to both sides: \[ 2 = -6 \] This is a contradiction, meaning that there is no solution where both equations hold true simultaneously.
Thus, the system of equations is inconsistent, and there are no values for \( x \) and \( y \) that satisfy both equations.