SOLUTION: 3x - 2y = 5 x - y = 0 solve the following pairs of simultaneous equations using the matrix method. give answers as ordered pairs (x, you)

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Question 1131435: 3x - 2y = 5
x - y = 0
solve the following pairs of simultaneous equations using the matrix method. give answers as ordered pairs (x, you)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
using inverse matrix:
3x+-+2y+=+5
x+-+y+=+0

A=matrix%282%2C2%2C3%2C-2%2C1%2C-1%29
and
B=matrix%282%2C1%2C5%2C0%29


A+is invertible and
A%5E-1=matrix%282%2C2%2C1%2C-2%2C1%2C-3%29

Then you get
X=A%5E1%2AB+=%28matrix%282%2C2%2C1%2C-2%2C1%2C-3%29%29*%28matrix%282%2C1%2C5%2C0%29%29

=matrix%282%2C1%2C1%2A5%2B%28-2%29%2A0%2C1%2A5%2B%28-3%29%2A0%29

= %28matrix%282%2C1%2C5+%2B+0%2C5+%2B+0%29%29
= %28matrix%282%2C1%2C+5%2C5%29%29:
x=+5
y=5

or using Cramer's rule:
∆ = +matrix%282%2C2%2C3%2C%09-2%2C%0D%0A1%2C%09-1%29=+-1

∆ [1]= +matrix%282%2C2%2C5%2C%09-2%2C%0D%0A0%2C%09-1%29=+-5

∆ [2]=++matrix%282%2C2%2C3%2C%095%2C%0D%0A1%2C%090%29=+-5

x=∆ [1]/∆ =-5%2F-1=5
y=∆ [2]/∆ =-5%2F-1=5