Question
list Is the ordered pair a solution to the given linear equation? \[ x+7 y=35,(0,5) \] no yes
Ask by Summers Colon. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ordered pair \((0, 5)\) is a solution to the equation \(x + 7y = 35\).
Solution
We need to check whether the ordered pair \((0, 5)\) satisfies the equation \(x + 7y = 35\).
1. Substitute \(x = 0\) and \(y = 5\) into the equation:
\[
0 + 7(5) = 0 + 35 = 35
\]
2. Since the left-hand side equals the right-hand side (\(35 = 35\)), the ordered pair \((0, 5)\) is a solution to the equation.
The answer is: yes.
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Simplify this solution The Deep Dive
To check if the ordered pair (0, 5) is a solution to the equation \( x + 7y = 35 \), simply substitute \( x = 0 \) and \( y = 5 \) into the equation. This gives you \( 0 + 7(5) = 35 \), which simplifies to \( 35 = 35 \). Since both sides are equal, the ordered pair (0, 5) is indeed a solution to the equation – so the answer is yes! If you're ever unsure about whether a point is a solution, just plug it back into the equation! Remember, if both sides evaluate to the same number, you’ve got a winner! Common mistakes include miscalculating the left side or forgetting to use the correct values from the ordered pair. Always double-check your arithmetic for accuracy!
