3m-7n=-43 6m+5n=-10

Question

I need to find the matrix of these variables

Answer 1

3m-7n=-43

6m+5n=-10

Matrix is:

⌈3 -7 | -43 ⌉

⌊6  5 | -10  ⌋

To solve, find the determinant=3×5-(-7)×6=15+42=57.

Find the determinant for m:

⌈-43 -7 ⌉

⌊  -10  5 ⌋= -43×5-(-7)(-10)=-215-70=-285,

m=-285/57=-5.

Find the determinant for n:

⌈3 -43 ⌉

⌊6  -10 ⌋= 3(-10)-6(-43)=-30+258=228,

n=228/57=4.

CHECK

3m-7n=-15-28=-43,

6m+5n=-30+20=-10.

All OK.