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Sagot :
Change to slope-intercept form:
2x - 5y - 5 = 0
-5y = -2x + 5
-5y/-5 = -2x/-5 + 5/-5
y = ²/₅ x - 1
m = ²/₅ y-intercept = -1
3x - 7y -2 = 0
-7y = -3x + 2
-7y/-7 = -3x/-7 + 2/-7
y = ³/₇ x - ²/₇
m = ³/₇ y-intercept = -²/₇
ANSWER: The system is independent, because the pair of equation has different slopes and different y-intercepts.
Remember:
Independent system:
- different slopes
- different y-intercepts
- line intersects in a graph, therefore, has one solution
which is the point of intersection.
Dependent and consistent system:
- same slopes
- same y-intercepts
- the lines are overlapping or coinciding in the graph
- all the points on the overlapping graph are solution,
therefore, the system has many or infinite solutions.
Inconsistent system:
- different slopes
- different y-intercepts
- the lines are parallel in the graph
- no solution, because the lines do not meet at any point.
2x - 5y - 5 = 0
-5y = -2x + 5
-5y/-5 = -2x/-5 + 5/-5
y = ²/₅ x - 1
m = ²/₅ y-intercept = -1
3x - 7y -2 = 0
-7y = -3x + 2
-7y/-7 = -3x/-7 + 2/-7
y = ³/₇ x - ²/₇
m = ³/₇ y-intercept = -²/₇
ANSWER: The system is independent, because the pair of equation has different slopes and different y-intercepts.
Remember:
Independent system:
- different slopes
- different y-intercepts
- line intersects in a graph, therefore, has one solution
which is the point of intersection.
Dependent and consistent system:
- same slopes
- same y-intercepts
- the lines are overlapping or coinciding in the graph
- all the points on the overlapping graph are solution,
therefore, the system has many or infinite solutions.
Inconsistent system:
- different slopes
- different y-intercepts
- the lines are parallel in the graph
- no solution, because the lines do not meet at any point.
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