Question
The system of linear equations y = negative 3 x + 5 and y = negative 3 x minus 6 is graphed below.
On a coordinate plane, 2 lines are parallel to each other.
How many solutions does the system of equations have?
0
1
3
4
On a coordinate plane, 2 lines are parallel to each other.
How many solutions does the system of equations have?
0
1
3
4
Answers
Answered by
GPT-4o mini
The system of linear equations provided is:
1. \( y = -3x + 5 \)
2. \( y = -3x - 6 \)
Both equations are in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept.
In this case, both lines have the same slope of -3, which means they are parallel to each other. Since parallel lines do not intersect at any point, there are no solutions where the two equations are equal.
Therefore, the system of equations has **0 solutions**.
1. \( y = -3x + 5 \)
2. \( y = -3x - 6 \)
Both equations are in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept.
In this case, both lines have the same slope of -3, which means they are parallel to each other. Since parallel lines do not intersect at any point, there are no solutions where the two equations are equal.
Therefore, the system of equations has **0 solutions**.
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