Question
Find an ordered pair \( (x, y) \) that is a solution to the equation. \[ \begin{array}{l}x-3 y=6 \\ (x, y)=(1), \square\end{array} \]
Ask by Stuart Harris. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( (1, -\frac{5}{3}) \).
Solution
First, since the ordered pair has the form \((1, \square)\) and must satisfy the equation
\[
x - 3y = 6,
\]
we substitute \(x = 1\) into the equation:
\[
1 - 3y = 6.
\]
Next, subtract 1 from both sides to isolate the term with \(y\):
\[
-3y = 6 - 1 \quad \Longrightarrow \quad -3y = 5.
\]
Finally, divide both sides by \(-3\) to solve for \(y\):
\[
y = \frac{5}{-3} = -\frac{5}{3}.
\]
The ordered pair that is a solution to the equation is:
\[
(1, -\frac{5}{3}).
\]
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Simplify this solution Bonus Knowledge
To find the ordered pair \( (x, y) \) that is a solution to the equation \( x - 3y = 6 \) given \( (x, y) = (1, \square) \), let's substitute \( x = 1 \) into the equation. Starting from the equation: \[ 1 - 3y = 6 \] Now, isolate \( y \): \[ -3y = 6 - 1 \] \[ -3y = 5 \] \[ y = \frac{5}{-3} \] \[ y = -\frac{5}{3} \] Therefore, the ordered pair is \[ \boxed{\left(1, -\frac{5}{3}\right)}. \]
