SOLUTION: SOLVE BY SUBSTITUTION METHOD AND DETERMINE WHETHER ITS A INDEPENDENT, DEPENDENT, OR INCONSISTENT x=2y-7 3x+2y=-5

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Question 124031: SOLVE BY SUBSTITUTION METHOD AND DETERMINE WHETHER ITS A INDEPENDENT, DEPENDENT, OR INCONSISTENT
x=2y-7
3x+2y=-5
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!





Discussion







First off, please stop SHOUTING!



Definitions:



Consistent and dependent:  Identical slopes and intercepts, i.e. they are

the same line.  Infinite solutions

Consistent and independent:  Different slopes.  Intersect in one point.  One

solution.

Inconsistent:  Identical slopes, different intercepts.  Parallel lines. No

solution.












Solution









x=2y-7

3x%2B2y=-5



Since you have an expression that is equal to x, i.e. the first equation,

you can substitute this expression for x in the other equation

3%2Ared%28%282y-7%29%29%2B2y=-5





Solve for y:

6y-21%2B2y=-5

8y=-5%2B21

8y=16

y=2





Substitute this value for y into the first equation:

x=2%282%29-7

x=-3





So your solution is the ordered pair (-3,2)





Since there is only one solution, the system is consistent and independent.