Question
Does (6, 1) make the equation y = x2 + –2x true?
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Answered by
GPT-4o mini
To determine if the point (6, 1) makes the equation \( y = x^2 - 2x \) true, we can substitute \( x = 6 \) into the equation and check if it equals \( y = 1 \).
First, substitute \( x = 6 \) into the equation:
\[
y = 6^2 - 2(6)
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Next, calculate \( -2(6) \):
\[
-2(6) = -12
\]
Now, combine the two results:
\[
y = 36 - 12 = 24
\]
Since \( y = 24 \) when \( x = 6 \), we see that the coordinate \( (6, 1) \) does not satisfy the equation \( y = x^2 - 2x \) because \( 24 \neq 1 \).
Thus, the point (6, 1) does not make the equation true.
First, substitute \( x = 6 \) into the equation:
\[
y = 6^2 - 2(6)
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Next, calculate \( -2(6) \):
\[
-2(6) = -12
\]
Now, combine the two results:
\[
y = 36 - 12 = 24
\]
Since \( y = 24 \) when \( x = 6 \), we see that the coordinate \( (6, 1) \) does not satisfy the equation \( y = x^2 - 2x \) because \( 24 \neq 1 \).
Thus, the point (6, 1) does not make the equation true.
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