SOLUTION: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. -3x + y = 4 2x � 3y = 9

Question 207113: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.
-3x + y = 4
2x � 3y = 9

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

Start with the given system of equations:

Start with the first equation.

Add to both sides.

Rearrange the terms and simplify.

-------------------------------------------

Move onto the second equation.

Now plug in .

Distribute.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

-------------------------------------------

Since we know that , we can use this to find .

Go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

So the solutions are and .

which form the ordered pair (-3,-5)

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

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