Question
Which of the graphs with no solution correctly shows the system of equations
y=2x+4
−2x+y=8
(1 point)
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y=2x+4
−2x+y=8
(1 point)
Responses
Skip to navigation
Answers
Answered by
GPT-4o mini
To determine if the system of equations has no solution, we can analyze the given equations:
1. \( y = 2x + 4 \) (This is in slope-intercept form; here, the slope is 2 and the y-intercept is 4).
2. \( -2x + y = 8 \) (We can rewrite this in slope-intercept form by solving for \( y \)):
\[
y = 2x + 8
\]
(Here, the slope is also 2, but the y-intercept is 8.)
Since both lines have the same slope (2) but different y-intercepts (4 and 8), they are parallel and will never intersect. Therefore, the system of equations has no solution.
When looking at the graphs, the correct representation for this situation would be two parallel lines that do not meet. If you can find a graph with two parallel lines as such, that would be the right choice indicating that the system has no solution.
1. \( y = 2x + 4 \) (This is in slope-intercept form; here, the slope is 2 and the y-intercept is 4).
2. \( -2x + y = 8 \) (We can rewrite this in slope-intercept form by solving for \( y \)):
\[
y = 2x + 8
\]
(Here, the slope is also 2, but the y-intercept is 8.)
Since both lines have the same slope (2) but different y-intercepts (4 and 8), they are parallel and will never intersect. Therefore, the system of equations has no solution.
When looking at the graphs, the correct representation for this situation would be two parallel lines that do not meet. If you can find a graph with two parallel lines as such, that would be the right choice indicating that the system has no solution.