SOLUTION: the problem says solve each system of equations by substitution. -3x+y=-4 -2x+3y=9

Question 223201: the problem says solve each system of equations by substitution.
-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.

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

Now plug in into the second equation.

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.

Add to both sides.

Combine like terms on the right side.

So the answer is and .

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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