SOLUTION: Solve by the elimination method 2r-5s=-33 5r+2s=48 I think the answer is that there is no solution but I am not sure. Please someone help me to solve this

Question 388335: Solve by the elimination method
2r-5s=-33
5r+2s=48
I think the answer is that there is no solution but I am not sure. Please someone help me to solve this
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 2.

Distribute and multiply.

Multiply the both sides of the second equation by 5.

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 the solutions are and .

This means that the system is consistent and independent.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
RELATED QUESTIONS
Solve by elimination method 2r - 5s = -14 5r + 2s = 52 what is the solution of the... (answered by Maths68)

I have been working on a problem using the elimination method. I think I have it right... (answered by scott8148,stanbon)

Solve by the elimination method 2r-5s= -1 5r+2s=41 What is the solution of the system? (answered by ewatrrr)

Solve by the elimination method 5r-2s=0... (answered by Flannery)

Solve by the elimination method. 7r-3s=3 3r+7s=51 I think there is no solution but I'm (answered by mathie123,josmiceli)

What is the elimination method 2r-5s=-29 and... (answered by mananth)

I have worked this problem several times and just want to be sure I did it correctly. I... (answered by Fombitz,scott8148)

5r-2s=37 2r+5s=38 Solve using the elimination... (answered by stanbon)

``Solve by using the elimination method.2r-9s=-109r+2s=40 What is the solution of the... (answered by ankor@dixie-net.com)