Fuentes Deleon
05/26/2024 · Middle School
Determine whether each ordered pair is a solution of the given equation. \( y=\sqrt{x}+1 ;(1,2),(9,4) \)
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Step-by-step Solution
To determine whether each ordered pair is a solution of the equation \( y = \sqrt{x} + 1 \), we will substitute the \( x \) value from each ordered pair into the equation and see if the resulting \( y \) value matches the \( y \) value in the ordered pair.
1. For the ordered pair \( (1, 2) \):
- Substitute \( x = 1 \) into the equation:
\[
y = \sqrt{1} + 1 = 1 + 1 = 2
\]
- The calculated \( y \) value is 2, which matches the \( y \) value in the ordered pair \( (1, 2) \). Therefore, \( (1, 2) \) is a solution.
2. For the ordered pair \( (9, 4) \):
- Substitute \( x = 9 \) into the equation:
\[
y = \sqrt{9} + 1 = 3 + 1 = 4
\]
- The calculated \( y \) value is 4, which matches the \( y \) value in the ordered pair \( (9, 4) \). Therefore, \( (9, 4) \) is also a solution.
In conclusion, both ordered pairs \( (1, 2) \) and \( (9, 4) \) are solutions of the equation \( y = \sqrt{x} + 1 \).
Quick Answer
Both ordered pairs \( (1, 2) \) and \( (9, 4) \) are solutions of the equation \( y = \sqrt{x} + 1 \).
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