SOLUTION: how many solutions exist? 1. 3x-y=7 6x-2y=6 are the equations : consistent/inconsistent/dependent graphs of the lines are : intersect/parallel/coincide 2. 3x+2y=5 -x+5y

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Question 389307: how many solutions exist?
1.
3x-y=7
6x-2y=6
are the equations : consistent/inconsistent/dependent
graphs of the lines are : intersect/parallel/coincide
2.
3x+2y=5
-x+5y=7
are the equations : consistent/inconsistent/dependent
graphs of the lines are : intersect/parallel/coincide
3.
-x-2y=-3
3x+6y=9
are the equations : consistent/inconsistent/dependent
graphs of the lines are : intersect/parallel/coincide
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
1.
3x-y=7 ----> 6x - 2y = 14, after multiplying by 2.
6x-2y=6
The system is inconsistent. The lines are parallel.
2.
3x+2y=5
-x+5y=7
The system is consistent & independent. (The determinant of the coefficient matrix is non-zero.) The lines intersect.
3.
-x-2y=-3 --------> 3x + 6y = 9, after multiplying both sides by -3
3x+6y=9 (The two equations are the same!)
The system is dependent. The lines are coincident.
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