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

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
first equation
second equation
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

substitute in 1st for in second

The equations are independant
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 25 from both sides

Combine like terms on the right side

Divide both sides by -3 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and 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 of (red) and (green)

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