SOLUTION: solve the system using the linear combination method 4x+2y=2 5x-2y=-11

Algebra ->  College  -> Linear Algebra -> SOLUTION: solve the system using the linear combination method 4x+2y=2 5x-2y=-11      Log On


   

Question 218697: solve the system using the linear combination method
4x+2y=2
5x-2y=-11
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system using the linear combination method

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

This is the elimination method (don't know if that's what your teacher means by the linear combination method. I think this is ok because you are just taking a linear combination of Equations A and B to yield another equation).

Add the two equations A and B to ge 9x=-9 or x=-1. Substituting x=-1 into Equation A yields -4+2y=2 or 2y=6 and y=3.

So solution is (-1,3).

The following solves using the Substituion method with the same results.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++4%5Cx+%2B+2%5Cy+=+2%2C%0D%0A++++5%5Cx+%2B+-2%5Cy+=+-11+%29%0D%0A++We'll use substitution. After moving 2*y to the right, we get:
4%2Ax+=+2+-+2%2Ay, or x+=+2%2F4+-+2%2Ay%2F4. Substitute that
into another equation:
5%2A%282%2F4+-+2%2Ay%2F4%29+%2B+-2%5Cy+=+-11 and simplify: So, we know that y=3. Since x+=+2%2F4+-+2%2Ay%2F4, x=-1.

Answer: system%28+x=-1%2C+y=3+%29.



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