SOLUTION: Thanks in advance for anyone who can help me!! :) Solve using the addition method: x+3y=19 x-y= -1 Here's what I've done so far, I can't seem to get past it x+3y=19 x-y=

Question 182817This question is from textbook Prentice Hall Algebra 1
: Thanks in advance for anyone who can help me!! :)
Solve using the addition method:
x+3y=19
x-y= -1
Here's what I've done so far, I can't seem to get past it
x+3y=19
x-y= -1
and I added them so I have this: 2x+2y=18. I'm not even sure if that's right.
This question is from textbook Prentice Hall Algebra 1

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

Start with the given system of equations:

Multiply the both sides of the second equation by 3. The goal here is to get the "y" coefficients equal but opposite.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

Which form the ordered pair

.

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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