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A line has the equation z = -2y + z. If ...

A line has the equation `z = -2y + z`. If (3,2) is a point on the line, what is z?

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To solve the problem, we need to find the value of \( z \) given the equation of the line and a point that lies on that line. The equation of the line is given as: \[ x = -2y + z \] And the point provided is \( (3, 2) \). ### Step-by-Step Solution: 1. **Identify the equation and point**: The equation of the line is \( x = -2y + z \) and the point is \( (3, 2) \), where \( x = 3 \) and \( y = 2 \). 2. **Substitute the values of \( x \) and \( y \)**: We substitute \( x = 3 \) and \( y = 2 \) into the equation: \[ 3 = -2(2) + z \] 3. **Calculate the value of \( -2(2) \)**: Calculate \( -2(2) \): \[ -2(2) = -4 \] 4. **Rewrite the equation**: Substitute \( -4 \) back into the equation: \[ 3 = -4 + z \] 5. **Isolate \( z \)**: To find \( z \), add \( 4 \) to both sides of the equation: \[ 3 + 4 = z \] \[ z = 7 \] 6. **Conclusion**: Thus, the value of \( z \) is \( 7 \). ### Final Answer: The value of \( z \) is \( 7 \).
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