Respuesta :
Parallel because when you put it into y=mx+b form, it will have the same slope.
The correct classification of the system of equations is given below.
What is system of equations?
System of equation can be defined a set of two or more equations with the variables to be solved together.
System of equations can be classified as :
If lines are parallel, and equation have no solution, then the system is inconsistent. i.e. [tex](\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2} )[/tex]
If lines intersect in a single point, and equation have unique solution, then the system is consistent. i.e.[tex](\frac{a1}{a2} \neq \frac{b1}{b2} )[/tex]
If lines coincident, and equation have many solution, then the system is consistent and dependent. i.e. [tex](\frac{a1}{a2} = \frac{b1}{b2}= \frac{c1}{c2} )[/tex]
so, here we have,
[tex]y-3x=3[/tex]
[tex]y = 3x-2[/tex]
we can rewrite the above equation as ;
[tex]-3x+y-3=0[/tex]
[tex]3x-y-2=0[/tex]
as we can see that ,
[tex]a1=-3, b1=1, c1=-3[/tex]
[tex]a2=3, b2=-1, c2=-2[/tex]
from the above equation we can see that,
[tex](\frac{a1}{a2} = \frac{b1}{b2}\neq \frac{c1}{c2} )[/tex]
i.e. equation has no solution and lines are parallel.
Hence, we can say that correct classification of system of equation is Parallel lines with no solution.
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