SOLUTION: I am confused can someone help? I need to solve each system by the substitution method and determine if they are independent, dependent, or inconsistent. {{{2y=x+6}}} first line

Algebra ->  Linear-equations -> SOLUTION: I am confused can someone help? I need to solve each system by the substitution method and determine if they are independent, dependent, or inconsistent. {{{2y=x+6}}} first line      Log On


   

Question 124954: I am confused can someone help? I need to solve each system by the substitution method and determine if they are independent, dependent, or inconsistent.
2y=x%2B6 first line
-3x%2B2y=-2
thanks
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The given equations are:

2y = x + 6 ---------------(1)

-3x + 2y = -2 --------------(2)


Substituting (1) in (2) we get:

-3x + x + 6 = - 2

-2x = -2 - 6

-2x = -8

x = 4

By back substitution we get the "y" value:

2y = 10

==> y = 5

So we observe that the line intersects at (4,5) for both the graphs.

+graph%28+400%2C+400%2C+-20%2C+20%2C+-20%2C+20%2C+x%2F2+%2B+3%2C+1.5x+-1%29+

Hence the given system of equations are Consistent & Dependent

Thus the solution.


Here are the notes that will help you determine the category under which they fall.

If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.
If the two equations describe lines that intersect once, the system is independent and consistent.
If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent.