Bot GPT 4-o mini To find the solution to the system of equations \( y = x - 6 \) and \( y = -x + 4 \), we need to determine the point where these two lines intersect.
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Set the two equations equal to each other since both are equal to \( y \): \[ x - 6 = -x + 4 \]
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Solve for \( x \):
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Add \( x \) to both sides: \[ x + x - 6 = 4 \] \[ 2x - 6 = 4 \]
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Add 6 to both sides: \[ 2x = 10 \]
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Divide by 2: \[ x = 5 \]
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Now substitute \( x = 5 \) back into either of the original equations to find \( y \). We'll use the first equation: \[ y = 5 - 6 = -1 \]
Thus, the solution to the system of equations, or the intersection point, is \((5, -1)\).
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