Question
Which graph shows the solution of −3x−y=3
and y=−3x+4
?(1 point)
Responses
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
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and y=−3x+4
?(1 point)
Responses
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
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Answers
GPT-4o mini
To find which graph represents the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we can start by rearranging the first equation into slope-intercept form.
Starting with \(-3x - y = 3\):
1. Add \(3x\) to both sides:
\(-y = 3 + 3x\)
2. Multiply by -1 to solve for \(y\):
\(y = -3x - 3\)
Now, we have the two equations:
1. \(y = -3x - 3\) (Line 1)
2. \(y = -3x + 4\) (Line 2)
Both lines have the same slope of \(-3\), but different \(y\)-intercepts (-3 for Line 1 and 4 for Line 2). This means that the lines are parallel and will never intersect.
Given this information, the correct graph would be:
**"Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This indicates that the two lines do not intersect, confirming they are parallel.
Starting with \(-3x - y = 3\):
1. Add \(3x\) to both sides:
\(-y = 3 + 3x\)
2. Multiply by -1 to solve for \(y\):
\(y = -3x - 3\)
Now, we have the two equations:
1. \(y = -3x - 3\) (Line 1)
2. \(y = -3x + 4\) (Line 2)
Both lines have the same slope of \(-3\), but different \(y\)-intercepts (-3 for Line 1 and 4 for Line 2). This means that the lines are parallel and will never intersect.
Given this information, the correct graph would be:
**"Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This indicates that the two lines do not intersect, confirming they are parallel.