Question
1 Eq #2: Eq #1: the two equations; 3 Wns 1 Three tmes - 'J4a4} 1 94
1 Eq #2: Eq #1: the two equations; 3 Wns 1 Three tmes - 'J4a4} 1 94
Answers
$$\text { In Exercises } 1-14, \text { solve the system of equations using the elimination method.}$$ $$\left\{\begin{array}{r} x-3 y=1 \\ 2 x+y=9 \end{array}\right.$$
Alright. So to eliminate X from the third equation, we add blank times the first equation to the third equation. Okay, so this is the third equation. And this is the first and which I am to eliminate X. The debtor equation has three acts, and the first equation has X. So we have to add times the first equation. That's a blank times the first degrees into the dirt equation. So we basically have to multiply. Negative. Three, two. The first equation to get rid of the X. So this is ended up being stood up because negative three x plus Do your exes. You put yourself Okay, so it's multiplying in grade three. Time this equation X my swine. Christie, if you could do three, actually, that is not a three. Yeah, okay. And multiplying that out, we get negative. Great X minus, plus freeway. One is three C because you could see and live six. And that's still new equation. And we're going to add it to our third equations, which is three x. Yes. Why? Managed to, uh, anything good teacher. I don't miss you get negative. Three x plus three X, which is zero three y plus y, which is four y and look greasy. Man is Tuesday, which is a good five c in 96 but still which isn't good for.
Her. We have to solve the given system off equation by using elimination muttered. And then we have to check the solution also. So the given equations are one. Divide by two x plus one by three y is equal to minus two on the second equation is one by four x plus to buy three. Why is equal to minus five by two now? First of all, I'll clear the fractions off both. The question so that we can simplify the equation quickly aren't easily for that. I'll be multiplying the two equation with certain number and how to find that certain number for equation one. Disick or Asian will multiply the equation by the l seem off to 13 Lt means least common factor off, too on the treat, which is six. So I multiplied. Disa collision by six on for second equation will take the LC um off four and three four entry, which is a 12. So I'll multiply this equation by 12. After multiplication, we will get three X plus two. Why is equal to minus 12 on hair will get three X plus eight way is equal to minus 30. Now multiply this equation by minus one and let this equation be ours. Three. And let this equation B s for So are you multiplying the equation three with minus one. So I'll get minus three X minus two. Why is equals to 12 on second equation as it is three x plus a try as equals to minus 30. No, let's art board the equation. Her minus three x and plus tricks will cancel out that his wife will multiply the equation three with negative one sorted it. Can we cancel it out here when we are both the equation to this was the reason My multi for the multiplication off minus one Red equation three. So help me get zero on DDE. Six way as equals. Two minus 18. From here, the value off Why comes out? Two beers minus three now Other subsidiary ing the villi off. Why in equation three, you can substitute in question for old, so it's up to you. The solution or the result will remain the same. So I'll get three times over X mine. Ah bless. Two times off. Minus tree as equals two minus 12. So three x is it called to minus 12 plus six from her begin right three x is equal to minus six or expect sickles to minus two. Finally, the value of X comes out to be as minus two and really off. Why comes Arch to be as minus three? Now we'll be checking that the solution that we open is correct or not. For that, I'll be substituting these value in equation three. You can subsidiary in equation for old, so it's up to you. The solution will remain the same. So three times off, minus two. Bless two times off. Minus three is equal to minus 12. So herds minus six minus six is a girl to minus 12 on a minus tral physical minus 12. So the observed on the left side of the equation equals to the right side. Hence we can conclude that the value of X invited were pained is correct. I hope you got a problem. Thank you.
I'm gonna choose to solve this system using elimination, and I'm gonna choose to eliminate why, just because this one is easier to manipulate than either of the exes. So if the one above it is positive 2/3. Why, I want this one to be negative. 2/3. Why? So I'm gonna multiply the second equation by negative 2/3. So with this system, the first equation will stay the same. And then the second, we will have negative 4/3 X minus 2/3. Why is equal to positive for thirds. So I'm gonna add these two together, our white terms cancel out. And then when you add negative for thirds plus 1/4 you want to get a common denominator here and then there. Let's see invention. We will get negative 13 over 12 X, and that's equal to. And then we'll do three plus 4/3 which is 13 3rd Okay, so I'm gonna take this next part one step at a time. I'm going to start by multiplying by 12 on both sides. So we have negative 13 X equals 52 and then divide by negative 13 on both sides, and I find that X is equal to negative for to sell for why we can use any of the equations. But I'm gonna choose to use this 2nd 1 because there were no fractions in that one. So we would have to ex so two times negative for Plus why equals negative, too. That's negative. Eight plus y equals negative, too. Add eight to both sides and we get that. Why six So X is equal to negative for y is equal to six.
All right. So this question were given this system of equations here, and we were asked what happens when we add the first equation and times do through the second equation. So and we multiplied the first equation by do we get two times X minus Two times. Why? Plus two times Z equals four. Just multiplying. All the factors, my food and the second equation is my ex. Let's do I classy equals minus tree. So now we want to add these equations together, and we just do this. Um, they're my term. Sure, we get two x plus minus X minus X Bless you. Minus. Do I plus do I? Yes. Cozy, Less busy equals. We asked these with dinner for his ministry minus three. Be working shots. What? We just is through X minus X is just X minus two. I plus two, I zero. So there's nothing here. Um, to z z s through Z and on the right side of the equation, we have four minus three witches. One. This is a question we get. We as to the first question, uh, through the second equation