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Lemur [1.5K]
3 years ago
12

At the beginning of the week, Paloma opened a new box of 100 coffee creamers. Sixty-seven coffee creamers were used during the w

eek. Which equation could be used to find x, the number of coffee creamers left at the end of the week?
Mathematics
2 answers:
Sergio [31]3 years ago
8 0
The answer would be 100 - 67 = 33
alukav5142 [94]3 years ago
7 0
Is this what you’re looking for? 100 - 67 = x
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marin [14]

Answer:  The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation:  The given system of linear equations is :

2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.

Now, from equations (ii) and (iii), we have

x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.

From equations (iv) and (v), we get

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Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

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3 years ago
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