A solution to 2-variable systems
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A solution to 2-variable systems

[From: ] [author: ] [Date: 11-12-09] [Hit: ]
Multiply mC by the inverse of mA to get the answers.And multiply by the determinate,For simplicitys sake,Now multiply this by the third matrix,......
ax+by=c
dx+ey= f

What would be the general solution to this systems of linear equations using the variables..so what would x and y be?

Please help with step by step instructions! thanks!

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Try using matrices (we'll call them mA, mB, and mC):
[a b] + [x] =[c]
[d e] + [y] =[f]

Multiply mC by the inverse of mA to get the answers.
To get mA:
[e -b]
[-d a]
And multiply by the determinate, which is 1/(ad-bc)
For simplicity's sake, we're going to multiply the above matrix by the det and call it
[eD -bD]
[-dD aD]

Now multiply this by the third matrix, mC:
eD*c+(-bD*f)=x
-dD*c+aD*f=y

Points would be much appreciated cause this took a hell of a long time to type up ;)
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