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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by -2.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms.

Simplify.

Since is never true, this means that there are no solutions.

So the system is inconsistent.

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