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# use matrix to solve the system of equations?

how would you set up the matrix to solve

6x+5y=21

5x-4y=42

can someone please help me out? please and thank you:)

### 1 Answer

- cidyahLv 79 years agoFavorite Answer
6 5

5 -4

is the coefficient matrix

Find its inverse.

Its determinant is (6)(-4) -(5)(5) = -24-25=-49

inverse of

a b

c d

is

d/k -b/k

-c/k a/k

where k=-49

6 5

5 -4

Find the inverse:

[ -4/-49 5/49]

[5/49 -6/49] ---------------(1)

Multiply by

21

42 -------------(2)

[ -4/-49 5/49] [21]

[5/49 -6/49] [42]

x = (4/49)(21)+(5/49)(42) = 6

y = (5/49)(21)-(6/49)(42) = -3