In Exercises 31–42, solve by the method of your choice. Identify ...

Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2yx + 2y = 13

Accepted Answer

Hey everyone welcome back in this problem. We are asked to solve the following system. Okay? We're told that the system is five X equals 13 plus nine Y. And five X minus nine Y. Is equal to minus five. Okay, so let's go ahead and label these equations. So the first equation is five X equals 13 plus nine Y. And the second equation is five X minus nine. Y equals minus five. Okay, now we haven't been told which method to solve with. So we can use substitution or the elimination or addition method that it's called sometimes. Okay, we could use either method. What we see is we have five X here in both equations. So that would be an easy choice to use the elimination method. So if we subtract these two equations we can get rid of that five X, eliminate that five X. And solve for Y. Okay, we just want to write these equations in the same format first before we do that. Okay, so if we rewrite equation to okay, we can rewrite it as and we'll call it two stars. So its equation to rewritten five X is equal and we want it in the same format, we want the constant minus five. We're gonna move the minus nine Y to the right hand side becomes a plus nine Y. Okay, so now we're going to take equation one. Okay and we're going to subtract equation to star, essentially subtracting equation two. We've just rearranged it. So we have five X equals 13 plus nine Y. We're going to subtract five X equals minus five plus nine Y Now five X -5 X. That's going to give us zero. Okay. On the right hand side 13 minus negative five. Well that's gonna give us 18 and on the right again nine y minus nine. Y. Well that's gonna give us zero as well. So in this case we end up with an expression zero equals 18. Well that's false. Okay, that's a false statement. No matter what value of X or y. You plug into that equation zero is not equal to 18. And what this tells us is that we have no solution. Ok? No matter what value of X and Y. We choose, we cannot get a true statement. Okay? So the answer here is going to be d no solution. That's it for this one. Everyone. Thanks for watching.

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In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2yx + 2y = 13

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