SOLUTION: Heres another one and these are making me feel dumb!! Solve using the elimination method 3r-4s=5 4r+3s=15 Type an ordered pair. Either integer or fractions.

Question 299194: Heres another one and these are making me feel dumb!!
Solve using the elimination method
3r-4s=5
4r+3s=15
Type an ordered pair. Either integer or fractions.
Thanks again!!
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 first equation by 3.

Distribute and multiply.

Multiply the both sides of the second equation by 4.

Distribute and multiply.

So we have the new system of equations:

Why did we just do all that? You'll see below:

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.

Notice how the 's' terms add to 0 and cancel out. So we're now left with a simple equation with one unknown.

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 the solutions are and .

Which form the ordered pair

.

This means that the system is consistent and independent.

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