Question

What is the value for the coefficient determinant (D) in the following system?

4x – 3y = 16
3x + 7y = –25

Answer 1

im trying to finish a thirteen assignments on flvs as fast as possible i know how to do them im just trying to get some shortcuts asap sorry but ill rate you as best response though for the consideration...

Answer 2

I suppose you are trying to apply Linear Algebra. Indeed you can express a system as a linear transformation and consider the determinant of the matrix representation.

If the determinant is non-zero there is a unique solution and if it is zero there could either be multiple solutions or no solutions at all.

Answer 3

This is true because a non-zero determinant implies full rank which implies a one to one and onto linear transformation which implies a unique solution.

Answer 4

you check calculator my eye not see good

Answer 5

What he is looking for is a matrix representation of the system. I will show you how to set it up and compute the determinant.

Answer 6

I don't have good eye may be Alchemista show you

Answer 7

7* (4x – 3y = 16 ) 28x-21y=112
3* (3x + 7y = –25 9x+21y=-75
------------
37x+ 0y = 37
x= 37/37
x =1
substitution x = 1 find y
can you find y?

Answer 8

substitution x = 1 find y

4x – 3y = 16
3x + 7y = –25

Answer 9

dannycobb5215 are you able find y?

Answer 10

go back original equation substitution x=1 than solve for y
4x – 3y = 16
3x + 7y = –25
use first or second equation

Answer 11

First we rewrite the system.
$$\left(\begin{array}{cc}
4 & -3 \\
3 & 7
\end{array}\right)
\left(\begin{array}{c}
x \\ y
\end{array}\right) =
\left(\begin{array}{c}
16 \\ -25
\end{array}\right)$$
Computing the determinant of a \(2 \times 2\) matrix is rather easy.
$$\textbf{det }\left(\begin{array}{cc}
a & b \\
c & d
\end{array}\right) = ad - bc$$
Now we compute the determinant of the system above.
\((4 \cdot 7) - (-3 \cdot 3) = 37\)
A non-zero determinant, therefore the system has a unique solution.

Answer 12

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Answer 13

You didn't read his question: "What is the value for the coefficient determinant (D) in the following system?"

He didn't ask for a solution to the system, he asked for the so called "coefficient determinant".