SOLUTION: Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answe

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answe      Log On


   

Question 161718: Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x,y).
If not, specify whether the answer is "no solution" or infinitely many solutions."
5x-4y=1
-10x+8y=-3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
system%285x-4y=1%2C-10x%2B8y=-3%29

To eliminate the terms in y, multiply the first equation
through by 2:

system%282%285x-4y%29=2%281%29%2C-10x%2B8y=-3%29

system%2810x-8y=2%2C-10x%2B8y=-3%29

Now add corresponding terme vertically:

system%28cross%2810x%29-cross%288y%29=2%2Ccross%28-10x%29%2Bcross%288y%29=-3%29

0=-1

Since all the variables cancelled out leaving only
numbers, and the resulting numerical equation is 
FALSE, the system is said to be INCONSISTENT, and
has NO SOLUTION. 

[Note: If all the variables had cancelled out leaving 
only numbers, and the resulting numerical equation had 
been TRUE instead of FALSE, then the system would have 
been DEPENDENT, and the system would have INFINITELY
MANY SOLUTIONS.]

Edwin