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Create a second equation SO the system has no solutions.=0.75x - 4...

Question

Create a second equation SO the system has no solutions.=0.75x - 4

Create a second equation SO the system has no solutions. =0.75x - 4



Answers

Find a system of equations in three variables that has exactly two equations and no solution.

Given that two x equal to four minus by and minus off by equal to two X minus two Leslie, convert these two equations in destined reform. So we get to eggs blessed by equally before and second equation becomes minus two X minus Y equal toe minus up to know every these two equations So two X minus two X s can salute by minus one is considered. So that site is zero equal before minus True, we get toe so we care. Zero equals toe. Too much is not possible. Instant given system is inconsistent and having no solutions.

This problem is asking waas writer system of equations that does not have a unique source for this problem. We just need to know three things. Number one one is you could to zero, and one is you go to one. Kill me. Put all the tips first. Um, number two Jiro is you could to one and number three. The last one you is equal to zero. And here I'm gonna put X the left side. Since this is metric from okay, number one if it so to get zero x should be you here and to get one X should be one here. So number one is for unique solution. Unique. Right? But this question is asked the question is asking us to find equations that does not have a unique solution. That means, um that means it's gonna be two and three. So here, that's put X. So to get one. Whatever. Leave put any numbers in here, you're not gonna get one. That means this number two has no solutions. Okay, Number three. Same thing. But you put ex here and is same thing here to get zero. It doesn't matter what we put here. We're gonna get zero anyway, because this is you. Right? So this gonna be infinite solution. So if he make metrics for number two, we can make something like this, you know, 101 So 00 this Ever quit Fisher. And here is gonna be a constant metric school. It's the you, but one. And what? So you is not equipped? One. So, this matrix that's gonna be it. No solution. And for number three Oh, I have to put red here. Okay, Okay. Problem number three. Same thing 10 and I'm gonna put 00 Well, im oppa zero here. All right, So zero is equal to zero. That means here is going to infinite solutions.

All right. So if I was given a linear equation, this guy and I was asked pick another one to make it make it into a system where there would be no solution where they would never intersect. Okay, easy enough. Um So let's first get this into a way I can read it. So I'm going to subtract X. Get wise is equal to 4 -1. Here. Okay, now I can read this and if I want to make it, so two lines never intersect. I keep the same slope and change the y intercept that is going to make the two lines parallel. Right? So you pick a you can pick any number you want. So if I Do, Why is equal to two -X? Okay? You just change your y intercept. They're never going to touch each other. That's that's the easiest way to make sure they never will. And I'll show you right here. Or even graph them, so you can verify that. So this one's Y intercept us for He gave it a one And it's going to give you a three. This one's will intercept us too. Two. You give it a one and it's going to give you one. And as you can see since they have the same slope, these two are never ever ever gonna touch each other, we're going to just keep going with the same slope in the same direction forever. And that's how you would you would pick your 2nd 1. So uh if I was doing this question um My 2nd 1 would just be Why is equal to two -X. Okay. Cool.

In order to solve this linear system of equations, I'm going to be using the elimination method to use elimination method. I need opposite coefficients now. I don't have that. So what I'm gonna have to do is multiply the top equation by two. There's a couple different ways that you could go about this. This would probably the easiest. So let's go ahead and distribute the two to each term in my equation and I'm gonna rewrite this off to the side. So now I have four X minus two. Why equals zero? My second equation stayed the same. Now look what happened. I have a negative to Why, in a positive to why those air opposite coefficients. So when I go to use the elimination method and I add them together, they will cancel out. So now I'm left with eight. X equals 12. Now I need to isolate my variable and divide by eight. And this gives me one and 1/2 or 3/2. Next, I need to find why. So I'm going to use the first equation and plug in what I found for acts which was 3/2 and solve for why So two times 3/2 is just three. Now I need to subtract three from both sides. So I have negative. Why equals negative three. Now I need to divide by a negative one to both sides. So I'm left, which is why equals three.


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