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4 years ago

A. 5b. 19c. -11d. 25

Mathematics

1 answer:

umka2103 [35]4 years ago

7 0

Answer:

The answer is d. 25

Step-by-step explanation:

a=-3,b=-7,c=-15

|a+b|+|c|

=|-3-7|+|-15|

=|-10|+|-15|

=10+15

=25

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Cramer's rule defines the solution of a system of equations in the following way:

$x= \frac{D_x}{D}$ , $y= \frac{D_y}{D}$ and $z= \frac{D_z}{D}$ where $D_x$ , $D_y$ and $D_z$ are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively. $D$ is the determinant of the system. Let's see how this rule applies to this system.

The system can be written in matrix form like:

$\left[\begin{array}{ccc}5&-3&1\\0&2&-3\\7&10&0\end{array}\right]\times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}6&11&-13\end{array}\right]$

Then each of the previous determinants are given by:

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$D_y = \left|\begin{array}{ccc}5&6&1\\0&11&-3\\7&-13&0\end{array}\right|=-398$ Notice how the y-column has been substituted with the answer-column one.

$D_z = \left|\begin{array}{ccc}5&-3&6\\0&2&11\\7&10&-13\end{array}\right|=-995$

Then, substituting the values:

$x= \frac{D_x}{D}=\frac{199}{199}\\ x=1$

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$x= \frac{D_z}{D}=\frac{-995}{199}\\ x=-5$

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