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In part (a) we found that the system of equations that corresponds to the given data is the following. $x + y = 50,000$ $z + w = 60,000$ $y + z + w = 90,080$ $x + y + z + w = 110,000$ We are given the extra fact that 11,920 more 12th graders vaped than 8th graders. Recall that the number of 12th graders who vaped is represented by the variable $z$ and the number of 8th graders who vaped is represented by the variable $x$. Then the linear equation that corresponds to the extra fact is $\boxed{z - x = 11,920}$. Form the augmented matrix associated with the new system of five linear equations in four variables. $\begin{bmatrix} 1 & 1 & 0 & 0 & 50,000 \\ 0 & 0 & 1 & 1 & 60,000 \\ 0 & 1 & 1 & 1 & 90,080 \\ 1 & 1 & 1 & 1 & 110,000 \\ -1 & 0 & 1 & 0 & 11,920 \end{bmatrix}$

          In part (a) we found that the system of equations that corresponds to the given data is the following.
$x + y = 50,000$
$z + w = 60,000$
$y + z + w = 90,080$
$x + y + z + w = 110,000$
We are given the extra fact that 11,920 more 12th graders vaped than 8th graders. Recall that the number of 12th graders who vaped is represented by the variable $z$ and the number of 8th graders who vaped is represented by the variable $x$. Then the linear equation that corresponds to the extra fact is $\boxed{z - x = 11,920}$.
Form the augmented matrix associated with the new system of five linear equations in four variables.
$\begin{bmatrix}
1 & 1 & 0 & 0 & 50,000 \\
0 & 0 & 1 & 1 & 60,000 \\
0 & 1 & 1 & 1 & 90,080 \\
1 & 1 & 1 & 1 & 110,000 \\
-1 & 0 & 1 & 0 & 11,920
\end{bmatrix}$

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in part a we found that the system of equations that corresponds to the given data is the following x y 50000 z w 60000 y z w 90080 x y z w 110000 we are given the extra fact that 11920 more 17494

Added by Alejandro W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Craig West

03/09/2023

Step 1

This translates to: $z - x = 11920$ (5) Show more…

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In part (a) we found that the system of equations that corresponds to the given data is the following. $x + y = 50,000$ $z + w = 60,000$ $y + z + w = 90,080$ $x + y + z + w = 110,000$ We are given the extra fact that 11,920 more 12th graders vaped than 8th graders. Recall that the number of 12th graders who vaped is represented by the variable $z$ and the number of 8th graders who vaped is represented by the variable $x$. Then the linear equation that corresponds to the extra fact is $\boxed{z - x = 11,920}$. Form the augmented matrix associated with the new system of five linear equations in four variables. $\begin{bmatrix} 1 & 1 & 0 & 0 & 50,000 \\ 0 & 0 & 1 & 1 & 60,000 \\ 0 & 1 & 1 & 1 & 90,080 \\ 1 & 1 & 1 & 1 & 110,000 \\ -1 & 0 & 1 & 0 & 11,920 \end{bmatrix}$

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Transcript

00:01 So this question, we're given the table of data.

00:04 And this is on a study done on 10th graders in u .s.

00:08 And europe.

00:09 And the question was, were they smoked or not smoked? and so you can see in this last column we have totals.

00:14 In the bottom row, we have totals, but we're missing one.

00:16 But we can easily do that by doing the $11 ,000 minus this 66 ,210.

00:23 And we get 44 ,000, or 880.

00:30 And so the first thing i asked is to write a system of equations.

00:33 Well, we can write a system of equations using that top row there where we have the x plus y equals 13 ,000.

00:42 And we can use the second row where we have z plus w equals 98 ,000.

00:53 And then we can use the first column.

00:55 So x plus z equals 44 ,880.

01:04 And then the second column, y plus w plus w.

01:11 Equals 66 ,210, right? and it says, well, does this system have a, have a unique solution and definitely not, it has infinitely many solutions? and you can see here it's based on, if i say the x is 1 ,000 here, right? that would, the y would change with respect to that, and so would the z.

01:33 Well, if i said that the x is 700, same thing, the y would change on that.

01:40 So you can see, that there's definitely not a unique solution here, this being a table.

01:45 And then the third part of the first question is, does this, or does this indicate about the data? well, we can't, we can't, from what we have right now, we can't determine what x, y, and z are, x, y, z or w is.

01:57 Right, we can't determine what those are.

01:59 So then part b, it says, given that 3 ,000, sorry, 39 ,000, 1010 more european 10th graders smoke than u .s...

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