SOLUTION: what is the solution for the equation 3x+y=6 2x-9y=5 using Co factor rule and the Cramer rule

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Question 1126288: what is the solution for the equation
3x+y=6
2x-9y=5
using Co factor rule and the Cramer rule
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

using the Cramer rule
Consider the system
a%5B1%5Dx%2Bb%5B1%5Dy=c%5B1%5D
a%5B2%5Dx%2Bb%5B2%5Dy=c%5B2%5D
Let the three determinants D,+Dx, and Dy be defined as

D=matrix%282%2C2%2Ca%5B1%5D%2Cb%5B1%5D%2Ca%5B2%5D%2Cb%5B2%5D%29
Dx=matrix%282%2C2%2Cc%5B1%5D%2Cb%5B1%5D%2Cc%5B2%5D%2Cb%5B2%5D%29
Dy=matrix%282%2C2%2Ca%5B1%5D%2Cc%5B1%5D%2Ca%5B2%5D%2Cc%5B2%5D%29

Then, if D%3C%3E0 the system has a unique solution of

x=Dx%2FD and y=Dy%2FD

given:
3x%2By=6
2x-9y=5+

D=matrix%282%2C2%2C3%2C1%2C2%2C-9%29=3%28-9%29-1%2A2=-27-2=-29

Dx=matrix%282%2C2%2C6%2C1%2C5%2C-9%29=6%28-9%29-1%2A5=-54-5=-59

Dy=matrix%282%2C2%2C3%2C6%2C2%2C5%29=3%2A5-6%2A2=15-12=3

x=Dx%2FD->x=-59%2F-29->x=59%2F29
and
y=Dy%2FD->y=3%2F%28-29%29->y=-3%2F29