Question
Find an ordered pair \( (x, y) \) that is a solution to the equation. \( \begin{array}{l}6 x+y=7 \\ (x, y)=(\square, \square)\end{array} \)
Ask by Bowers John. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
One solution is \( (1, 1) \).
Solution
To find an ordered pair \( (x, y) \) that is a solution to the equation \( 6x + y = 7 \), we can express \( y \) in terms of \( x \) and then choose a value for \( x \) to find the corresponding \( y \).
1. Start with the equation:
\[
6x + y = 7
\]
2. Rearranging the equation to solve for \( y \):
\[
y = 7 - 6x
\]
Now, we can choose a value for \( x \) to find \( y \). Let's choose \( x = 1 \):
3. Substitute \( x = 1 \) into the equation for \( y \):
\[
y = 7 - 6(1) = 7 - 6 = 1
\]
Thus, when \( x = 1 \), \( y = 1 \). Therefore, one ordered pair that is a solution to the equation is:
\[
(x, y) = (1, 1)
\]
So, the final answer is:
\[
(x, y) = (1, 1)
\]
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Simplify this solution Extra Insights
To find an ordered pair \( (x, y) \) that satisfies the equation \( 6x + y = 7 \), we can select a value for \( x \) and then solve for \( y \). Let's pick \( x = 1 \): Substituting \( x = 1 \) into the equation: \[ 6(1) + y = 7 \] This simplifies to: \[ 6 + y = 7 \] Now, isolate \( y \): \[ y = 7 - 6 = 1 \] Thus, one ordered pair solution is: \[ (x, y) = (1, 1) \] So the solution is \( (x, y) = (1, 1) \).
