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Makro · Answer 1 · 2023-06-02T23:13:16+0000

Step-by-step explanation

Given the system of equations:

(1) x +2y = 5

(2) x -3y = 7

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$
$=1\cdot \left(-3\right)-2\cdot \:1$

Remove parentheses:

$=-1\cdot \:3-2\cdot \:1$
$\mathrm{Multiply\:the\:numbers:}\:1\cdot \:3=3$
$=-3-2\cdot \:1$
$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2$
=-3-2

$\mathrm{Subtract\:the\:numbers:}\:-3-2=-5$
=-5

In conclusion, the determinant is -5

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