By using determinants, solve the following system of equations: `x+y+z=1` `x+2y+3z=4` `x+3y+5z=7`

Explanation

`x+y+z=1`

`x+2 y+3 z=4`

`x+3 y+5 z=7`


`D=|[1 , 1 , 1],[ 1 , 2 , 3 ],[ 1 , 3 , 5]|`
`=1(10-9)-1(5-3)+1(3-2)`
`=1-2+1=0`


`D_{1}=|[1 , 1 , 1 ],[ 4 , 2 , 3],[ 7 , 3 , 5]|=1(10-9)-1(20-21)+1(12-14)=1+1-2=0`


`D_{2}=|[1 , 1 , 1 ],[ 1 , 4 , 3],[ 1 , 7 , 5]|=1(20-21)-1(5-3)+1(7-4)=-1-2+3=0`


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