Question

Solve 3x – 7y = 25 5x – 8y = 27 using matrices. (25, 27) (27, 25) (-1, -4) (4, 1)

Answer 1

This is somewhat similar to something called Cramer's Rule http://www.1728.org/cramer.htm

A) 3x – 7y = 25
a =3 b=-7 e=25
B) 5x – 8y = 27
c=5 d=-8 f=27

dn = |a b |
        |c d |

dn = |3 -7|
       |5 -8

dn = (3*-8) -(5*-7)

dn = -24 +35

dn = 11

x = |e b|
      |f d|
divided by dn

x = |25 -7|
      |27 -8|
divided by dn

x = -200 -(-189) / 11
x = -11 / 11
x = -1

y = |a e |
     |c f |
divided by dn

y = |3 25|
     |5 27|
divided by dn

y = 81 -125 / dn = -44 / 11 =-4