Question

Lg(x-y+1)=0 and 1+lg (xy)=0,show x=y=1/√10

pls help I'm confused about how it works i kept getting 1/10.

Answer 1

Assuming
`\mathrm{lg}\,x=\log_(10)x`, you have from the first equation


`\mathrm{lg}(x-y+1)=0\implies 10^{\mathrm{lg}(x-y+1)}=10^0`

`\implies x-y+1=1\implies x-y=0\implies x=y`

From the second, you get


`1+\mathrm{lg}(xy)=0\implies\mathrm{lg}(xy)=-1\implies10^{\mathrm{lg}(xy)}=10^(-1)`

`\implies xy=\frac1{10}`

Since
`x=y`, you have


`x^2=\frac1{10}\implies x=y=\pm\frac1{√(10)}`