Question
c. \( \begin{array}{l}y=6 x+8 \\ y=6 x+13\end{array} \)
Ask by Mcdonald Rowe. in the United States
Feb 13,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The two equations are parallel and have no solution.
Solution
We are given the equations:
y = 6x + 8
y = 6x + 13
Since both lines have the same slope (6) but different y-intercepts (8 and 13), they are parallel.
To see this algebraically, set the two expressions equal:
6x + 8 = 6x + 13
Subtracting 6x from both sides gives:
8 = 13
This is a contradiction, meaning there is no value of x for which the equations are equal.
Thus, the system has no solution.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
These two equations represent parallel lines because they have the same slope of 6. While they will never intersect, they are separated by the difference in the y-intercepts (8 and 13). This means for any value of \( x \), the value of \( y \) in the second equation will always be 5 units greater than in the first equation. When graphing these lines, remember to plot points carefully. Start with the y-intercepts on the y-axis, which are at (0, 8) for the first line and (0, 13) for the second. Draw the lines extending in both directions, ensuring they remain parallel. A common mistake is to confuse slopes, so double-check that the slopes remain constant as you draw!
