Write the system in augmented-matrix form:
![\left[\begin{array}{ccc|c}2&2&4&16\\5&-2&3&-1\\1&2&-3&-9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D2%262%264%2616%5C%5C5%26-2%263%26-1%5C%5C1%262%26-3%26-9%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 1 by 1/2:
![\left[\begin{array}{ccc|c}1&1&2&8\\5&-2&3&-1\\1&2&-3&-9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C5%26-2%263%26-1%5C%5C1%262%26-3%26-9%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 1) to row 3, and add -5(row 1) to row 2:
![\left[\begin{array}{ccc|c}1&1&2&8\\0&-7&-7&-41\\0&1&-5&-17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C0%26-7%26-7%26-41%5C%5C0%261%26-5%26-17%5Cend%7Barray%7D%5Cright%5D)
Swap rows 2 and 3:
![\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&-7&-7&-41\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C0%261%26-5%26-17%5C%5C0%26-7%26-7%26-41%5Cend%7Barray%7D%5Cright%5D)
Add -7(row 2) to row 3:
![\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&0&-42&-160\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C0%261%26-5%26-17%5C%5C0%260%26-42%26-160%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 3 by -1/42:
![\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&0&1&\frac{80}{21}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C0%261%26-5%26-17%5C%5C0%260%261%26%5Cfrac%7B80%7D%7B21%7D%5Cend%7Barray%7D%5Cright%5D)
Add 5(row 3) to row 2:
![\left[\begin{array}{ccc|c}1&1&2&8\\0&1&0&\frac{43}{21}\\0&0&1&\frac{80}{21}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%262%268%5C%5C0%261%260%26%5Cfrac%7B43%7D%7B21%7D%5C%5C0%260%261%26%5Cfrac%7B80%7D%7B21%7D%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 2) and -2(row3) to row 1:
![\left[\begin{array}{ccc|c}1&0&0&-\frac53\\0&1&0&\frac{43}{21}\\0&0&1&\frac{80}{21}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%260%260%26-%5Cfrac53%5C%5C0%261%260%26%5Cfrac%7B43%7D%7B21%7D%5C%5C0%260%261%26%5Cfrac%7B80%7D%7B21%7D%5Cend%7Barray%7D%5Cright%5D)
So the solution to the system is
4=4 6=5 7=9 8=4 9=2 10=8 11=3 12=9
Note : Since unit of currency is not defined, I'll be using units.
Sales tax on a 15000 units car = 540 units
540 = 15000 × tax% / 100
=> 540 = 15000 × tax% / 100
=> 540/15000 = tax% / 100
=> tax% = (540/15000) × 100
=> tax% = 540/140
=> tax% = 3.6
now,
sales tax on a 32000 units car = 32000 × tax%/100
= 32000 × 3.6/100
= 320 × 3.6
= 1152 units
therefore sales tax on a 32000 units car = 1152 units
Each person will pay $115 because $1,380 divided by 12 is 115
