SOLUTION: Solve each system be the substitution method. Indicate whether each system is independent, inconsistent, or dependent. 3y = x+5 3x-9y = -10

Algebra ->  Linear-equations -> SOLUTION: Solve each system be the substitution method. Indicate whether each system is independent, inconsistent, or dependent. 3y = x+5 3x-9y = -10      Log On


   

Question 148040: Solve each system be the substitution method. Indicate whether each system is independent, inconsistent, or dependent.
3y = x+5
3x-9y = -10
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each system be the substitution method. Indicate whether each system is independent, inconsistent, or dependent.
3y = x+5
3x-9y = -10
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x = 3y-5
Substitute into 3x - 9y = -10 to solve for "y":
3(3y-5) - 9y = -10
9y - 15 -9y = -10
-15 = -10
This is false.
The system is inconsistent.
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%283y+=+x%2B5%2C3x-9y+=+-10%29


3y+=+x%2B5 Start with the first equation.


y=%28x%2B5%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%281%2F3%29x%2B5%2F3 Simplify.


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3x-9%28%281%2F3%29x%2B5%2F3%29+=+-10 Now plug in y=%281%2F3%29x%2B5%2F3 into the second equation.


3x-3x-15=-10 Distribute.


0x-15=-10 Combine like terms on the left side.


0x=-10%2B15 Add 15 to both sides.


0x=5 Combine like terms on the right side.


0=5 Simplify.


Since this equation is never true for any x value, this means that there are no solutions. So the system is inconsistent.