SOLUTION: Solve each system by the substitution method. determine whether the equstions are independent, dependent, or inconsistent. x=2y-7 3x+2y=-5

Question 121018: Solve each system by the substitution method. determine whether the equstions are independent, dependent, or inconsistent.

x=2y-7
3x+2y=-5
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

Add 21 to both sides

Combine like terms on the right side

Divide both sides by 8 to isolate y

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

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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