SOLUTION: without graphing tell whether the system of equations has a solution or no solution. 3x + y = 10 12x + 4y = 15 thank you!

Rule:  Given the system of equations:







It is one of the three:



1.  Independent system: There is exactly 1 solution if . 



(The graph of an independent system consists of two lines intersecting at 1

point.  They have one point in common, which represents the one solution) 



2.  Dependent system:  There are infinitely many solutions if .   



(The graph  of an dependent system consists of two lines which are one in the

same, that is, they coincide at every point, and their graphs are the same

line. That is, they have every point in common). 



3.  Inconsistent system:  There are no solutions if .   



(The graph  of an inconsistent system consists of two parallel lines, which of

course have no point in common).



In your system:







A=3, B=1, C=10, D=12, E=4, F=15















So yours is an inconsistent system.  (The graph therefore consists of two

parallel lines, which of course have no point in common, as shown below).