Simultaneous Equation Involving logarithm. CAN YOU SOLVE?

Simultaneous Equation Involving logarithm. CAN YOU SOLVE?
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[math]

very well done, your solution is easy to follow and understand

[mathematicsfundamental]

log(x+y)​ = 0
2logx = log(y+1)
———
x+y = 1
log x² = log(y+1)
x² = y+1
———
Isolate x for fiest equation
x = 1-y
then we substitute the equation in second equation
(1-y)²=y+1
y²-2y+1=y+1
y²-2y+1-y-1=0
y²-3y=0
y(y-3)=0
y = 0, 3
Substitute both y = 0 and 3 in any equations which I will choose x+y=1
x+0 = 1
x = 1 —> (1, 0)
x+3=1
x=1-3
x = -​2 —> (-2, 3)

so we get both (-2, 3) and (1, 0)
but since antilog > 0 soo (-2, 3) is not our solution and therefore, the actual answer is (1, 0)