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Solve system of linear equations, using ...

Solve system of linear equations, using matrix method,
`4x -3y = 3`
`3x -5y = 7`

Text Solution

Verified by Experts

Given system in the matrix form is
`[{:(4,-3),(3,-5):}][{:(x),(y):}]=[{:(3),(7):}]`
`rArr" "AX=B`
`rArr" "X=A^(-1)B`
`"Now, "A=[{:(4,-3),(3,-5):}]`
`|A|=[{:(4,-3),(3,-5):}]=-20+9=-11ne0`
`"and adj A"=[{:(-5,3),(-3,4):}]`
`therefore" "A^(-1)=1/|A|"adj.A=-1/11[{:(-5,3),(-3,4):}]`
Put in equation (1)
`X=A^(-1)B`
`[{:(x),(y):}]=1/11[{:(-5,3),(-3,4):}][{:(3),(7):}]`
`=1/11[{:(-15,+21),(-9,+28):}]=[{:(-6//11),(-6//11):}]`
`therefore" "x=-6/11" and "y=(-19)/11.`
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