Question

X + 2y = 5 x - 3y = 7 What is the value of the system determinant? 0-5 01

Answer 1

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