Solve each system of equations. State whether it is an inconsiste...

Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4.
9x - 5y = 1 
-18x + 10y = 1

Accepted Answer

Solve the following system of equations with two variables and determine if it is an inconsistent system or if it has infinitely many solutions write the solution set in terms of X. If it has infinitely many solutions where we have three, X minus seven, Y equals four and negative nine X plus 21 Y equals four. Now to solve this, we want to try to get rid of one of our variables. We're going to add these two equations together. We first need to multiply one of them to get rid of the variable. Let's say we get rid of X. We need to get rid of X by adding these two together. So let's multiply everything by positive three, we will get nine X minus 21 Y equals 12. And the other equation stays the same as negative nine X plus 21 Y equals four. We can now add these two equations together. We would get zero X plus zero, Y equals 16 or zero equals 16, zero equals 16 is a false statement. So we can determine then this has no solution, which is denoted as the empty set or an O with a slash to it, making this an inconsistent system. This means the answer to our problem is answer B ok. I hope to help you solve the problem. Thanks for watching. Goodbye.

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Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4. 9x - 5y = 1 -18x + 10y = 1