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Solve the following problem using the two phase methodmor z7x, Bxz 3x3Subject to371 +4x2 + 2x3 100 511 ` 6x3 > 55 3x1 + 4x2 = 70...

Question

Solve the following problem using the two phase methodmor z7x, Bxz 3x3Subject to371 +4x2 + 2x3 100 511 ` 6x3 > 55 3x1 + 4x2 = 70

Solve the following problem using the two phase method mor z 7x, Bxz 3x3 Subject to 371 +4x2 + 2x3 100 511 ` 6x3 > 55 3x1 + 4x2 = 70



Answers

Solve the equations for the variable.
$$13 z+6.45=8 z+23.75$$

Yeah. In order to solve this equation, the first thing that we have to do is get our variables on the same side. So we have 13 Z and a Z. We're going to take the smaller of those coefficients which is eight Z. And we're going to move it to the other side of the equation since it's a positive Z. In order to move it to the other side, we're going to be subtracting eight Z from both sides. And when we do that we can combine our like terms 13 Z minus eight Z is five, Z plus 6 45 equals 23 75. Now that we have our variables on the same side, we need to get our constant terms onto the same side. So um we need to move our 6.45 over to the other side and again that is being added, it's a positive 6.45 So we're going to subtract 6.45 from both sides. Mhm. Okay, so that leaves us with five. Z equals 17.3 When we combine those numbers together. Yeah. And then finally the last step to get the variable by itself, we have five times Z. So we're gonna divide both sides by five. So that gives us a solution of Z equals 3.46 And now we have to check our solution to do that. We're just going to go back to the original problem and we're gonna plug in this value that we got for Z 3.46 We're gonna plug that into the Z terms in the equation. Yeah. So when we plug that in we're going to have 13 times 3.46 plus 6.45 equals eight times 3.46 plus 23.75 So the next thing we need to do is perform these operations were going to start with the multiplication. So 13 times 3.46 is 44.98 Yeah plus 6.45 And then eight times 3.46 is 27.68 plus 23.75 So now the last step is just going to be to combine the terms on each side. So on the left, when we add these numbers together, we get 51 0.43 and on the right, when we add those together, we also get 51.43 So since we got the same number on both sides, that means that our answer checks out. So our original solution that we found the equals 3.46 is the correct solution for this equation, mm hmm.

All right. So this problem is asking us to solve for the variable the first thing I want to do. All right, So I have nine z plus two, and I like to think of the equal sign is kind of like a divider, right? And they're equal to seven z plus six. Okay, so the first thing I want to do is I want to get all of disease on one side. I want to get all disease on one side. Right. So I am going to subtract theseventies from over here, and so I have to do the same over here. Okay. So, mind Z, take away seven z gives me to Z. You're gonna bring down this plus two because I haven't used it yet. And on this side seven z minus seven z gives me zero, and I still have to bring this six down, so I have a six over here. All right, Now I want to get this disease by itself. I need to get rid of this plus two. And the way I do that is I'm gonna do the opposite. So the opposite of plus two would be to do minus two and whatever I do on this side of my equal sign right here, I have to do the same over here to keep it balanced. Right? So nothing going on here, I'm just gonna bring it down. This is two minus two. So that zero that's all gone and six minus two would give me for So this is still here. All right, So I still don't have that is you by itself. I need to get rid of this, too. So I see Two times, e. Right. So the opposite of that would be to divide by two If I divide by two here, have to do the same over here. Okay, so on this side, all I have left a Z equals and four divided by two gives me too. So there's my final answer.

I disagree. Algebraic Lee. So first we can do what we can do is subtracted 70 from both sides. You get to Z plus two equals six and now we can subtract two from both sides. Now we get to Z equals four equals four. So now let's divide both sides by two and we get Z equals four halves, which is too so Z equals two.

1 61 we have 6.6 x minus 18.9 equals 3.4 x plus 57 54 were 0.7. So first I'm going to subtract three point for X from both sides, so 6.6 x minus 3.4 x is 3.2 x minus 18.9 equals 54 quite seven. To get the X by itself, I have to add the 18.9 to both sides That becomes a C brow. So I have 3.2 x equals nine and seven and 16 eaten for his 12 13 five and one is six. That would be seven. Divide both sides by 3.2, divided by 3.2. So I have 73.6, divided by three point to move this over. One. Move this over one 32 goes into 73 twice that becomes 64. Bring down some 64 from 73 is nine. Bring down the six 32 goes into 96 3 times and that becomes a zero. So ex equals 23


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