SOLUTION: Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations? 2x+ y= 5 4x+ 3y= 11 Is the solution (2,1) or am I wrong? thank you.

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Question 218305: Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations?
2x+ y= 5
4x+ 3y= 11
Is the solution (2,1) or am I wrong? thank you.
Found 2 solutions by solver91311, drj:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Multiply the first equation by -3 giving you:



Now the coefficient on in the new first equation is the additive inverse of the coefficient on in the second equation. The multiplier in the first step was selected for the purpose of obtaining this result. Add the two equations, term-by-term:



Notice that the -terms have been eliminated, hence the name of the method.





Two ways to proceed from here:

Go back to the original set of equations and multiply the first by -2:



Again, add term by term:



This time eliminating the -terms



OR:

Just take the value you got for , namely and substitute it into either of the original equations, then solve for :





In either case, the solution you presented was correct, namely (2, 1).


John

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations?

2x+ y= 5 Equation A
4x+ 3y= 11 Equation B

Is the solution (2,1) or am I wrong? thank you.

Step 1 Check (2,1) by substituting into Equations A and B where x=2 and y=1.

2*2+1= 5 or 5=5 which satisfies Equation A.

4*2+3*1=8+3=11 of 11=11 which satisfies Equation B.

Step 2. The elimination method in this example means when you multiply either Equation A or B by a factor such that when you add or subtract these two equations, one of the variables x or y will be eliminated. When you eliminate a variable, then you have an equation with one variable in this case.

Step 3. As an example, take Equation A and multiply by -2. This yields

-4x-2y=-10 Equation A1
4x%2B3y=11 Equation B

Now when you add these two equations A1 and B, this will yield

-4x%2B4x-2y%2B3y=-10%2B11

y=1 This leaves a single equation with y=1.

Step 4. As another example take Equation A and multiply by -3. This yields

-6x-3y=-15 Equation A2
4x%2B+3y=+11 Equation B

Adding these two Equations A2 and B yields

-6x%2B4x-3y%2B3y=-15%2B11

-2x=-4 where we eliminated the y-terms and have a single variable in the equation.

Now divide -2 to both sides of the equation

x=2

So the solution is x=2 and y=1 or at point (2,1) as a solution given earlier in the problem.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV