SOLUTION: Can someone help? I am understanding part of the problem but not the whole problem. I feel like I am missing something..thanks Solve each system by the substitution method. Dete

Algebra ->  Linear-equations -> SOLUTION: Can someone help? I am understanding part of the problem but not the whole problem. I feel like I am missing something..thanks Solve each system by the substitution method. Dete      Log On


   

Question 124483: Can someone help? I am understanding part of the problem but not the whole problem. I feel like I am missing something..thanks
Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent..Thanks
y=x-5 first equation
2x-5y=1 second equation
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x+-+5
2x+-+5y+=+1
substitute y in 1st for y in second
2x+-+5%28x+-+5%29+=+1
2x+-+5x+%2B+25+=+1
-3x+=+-24
x+=+8
y+=+x+-+5
y+=+8+-+5
y+=+3
The equations are independant

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x-5y=1
y=x-5



2x-5%28x-5%29=1 Plug in y=x-5 into the first equation. In other words, replace each y with x-5. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x-5x%2B25=1 Distribute


-3x%2B25=1 Combine like terms on the left side


-3x=1-25Subtract 25 from both sides


-3x=-24 Combine like terms on the right side


x=%28-24%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=8 Divide




Now that we know that x=8, we can plug this into y=x-5 to find y



y=%288%29-5 Substitute 8 for each x


y=3 Simplify


So our answer is x=8 and y=3 which also looks like


So because we got a unique solution, this means that the system is independent.


Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+10%2C+-5%2C+8%2C+%281-2x%29%2F%28-5%29%2C+y=x-5%29+ Graph of 2x-5y=1 (red) and y=x-5 (green)