You spend $264 on clothes. shirts cost $24 and pants cost $32. you buy a total of 9 items. write a system of linear equations that represents this situation show work if you can.

Linear equations can also be referred to as Algebraic equations. Algebraic or Linear equations are equations that contain unknown variables. These unknown variables can be represented using the letters of the alphabet.

The system of linear equations that represents this situation is given as:

s + p = 9

24s + 32p = 264

Let's represent:

The number of shirts bought  = s

The number of pants bought = p

From the question, You buy a total of 9 items.  This statement can be represented using the linear equation below:

s + p = 9 Equation 1

Also, you spend $264 on clothes. The Shirts cost $24 and the pants cost $32. This statement can be represented using the linear equation below:

$24 x s + $32 x p = $264

24s + 32p = 264 Equation 2

Since: s + p = 9

s = 9 - p

To solve for p, we substitute 9 - p for s in equation 2

24(9 - p) + 32p = 264

216 -26p + 32p = 264

Subtract 234 from both sides

216 - 216 - 26p + 32p = 264 - 216

6p = 48

Divide both sides by 6

6p/6 = 48/6

p = 6

The number of pants you bought is 6.

To solve for s

s = 9 - p

s = 9 - 6

s = 3

The number of shirts you bought is 3.

Therefore, the system of linear equations that represents this situation is given as:

s + p = 9

24s + 32p = 264

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option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,