SOLUTION: solve the following systems of equations by elimination. verify the solutions. 4m-3n=27 8m-6n=18

Algebra ->  Linear-equations -> SOLUTION: solve the following systems of equations by elimination. verify the solutions. 4m-3n=27 8m-6n=18      Log On


   

Question 1090299: solve the following systems of equations by elimination. verify the solutions.
4m-3n=27
8m-6n=18
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
4m-3n=27
8m-6n=18
multiply top by -2 and add the two equations
-8m+6n=-54
8x+6n=36
0=-18
no solution.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
4m - 3n = 27     (1)
8m - 6n = 18     (2)


Left side of the equation (2) is doubled left side of the equation (1).

But the right side of the eq(2) is not doubled right side of the equation (1).


Therefore, the system CAN NOT and DOES NOT HAVE a solution.


Lesson to learn from this solution: 

     Learn how to analyse a given system of equations before (and without) solving it.


See the lesson
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".