Thread: Solve each of the following systems by addition

If a unique solution does not exist, state whether the system is inconsistent or dependent.


1. 2x + 3y = 1
5x + 3y = 16

This is what I came up with, but I can not seem to make it work so I think the equation is inconsistent. Am I right or wrong? I didn't want to try question #2 because I am having a hard time with #1


2x + 3y = 1
-5x - 3y = -16
-3x =-15
x= 5





2. x + 5y = 10
-2x -10y = -20

Originally Posted by Patience

If a unique solution does not exist, state whether the system is inconsistent or dependent.


1. 2x + 3y = 1
5x + 3y = 16

This is what I came up with, but I can not seem to make it work so I think the equation is inconsistent. Am I right or wrong? I didn't want to try question #2 because I am having a hard time with #1


2x + 3y = 1
-5x - 3y = -16
-3x =-15
x= 5





2. x + 5y = 10
-2x -10y = -20

There is nothing wrong with your analysis of #1. After adding, you (correctly) got x=5. All that's left to do is substitute 5 back into either of the original equations to find the y value of the point.

As for the second, you should notice that the second equation is simply the first with eqch term multiplied by -2. Divide both sides by -2 and you will have two of the same equation. Since they are the same line, any point on that line satisfies both and the system is therefore depenent.

-Pulsar