SOLUTION: without graphing, solve each equation and determine whether each system has no solution, one solution or an infinite number of solutions 5x-8y=24 10x-16y= -9

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: without graphing, solve each equation and determine whether each system has no solution, one solution or an infinite number of solutions 5x-8y=24 10x-16y= -9      Log On


   

Question 243674: without graphing, solve each equation and determine whether each system has no solution, one solution or an infinite number of solutions
5x-8y=24
10x-16y= -9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%285x-8y=24%2C10x-16y=-9%29


-2%285x-8y%29=-2%2824%29 Multiply the both sides of the first equation by -2.


-10x%2B16y=-48 Distribute and multiply.


So we have the new system of equations:
system%28-10x%2B16y=-48%2C10x-16y=-9%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-10x%2B16y%29%2B%2810x-16y%29=%28-48%29%2B%28-9%29


%28-10x%2B10x%29%2B%2816y%2B-16y%29=-48%2B-9 Group like terms.


0x%2B0y=-57 Combine like terms.


0=-57Simplify.


Since 0=-57 is never true, this means that there are no solutions.


So the system is inconsistent.