Which of the following is true about the system of equations

Which of the following is true about the system of equations given by: {10^x + 10^y = 5 10^x - 10^y = -3 A. The solution lies above the x-axis B. The solution lies below the x-axis C. The solution lies on the x-axis D. There is no solution E. There are infinitely many solutions

Solution

10^x +10^y = 5

10^x -10^y = -3

Add the two : 2*10^x = 2

10^x = 1

10^x = 10^0

x =0

Now plug x=0 to find y: 10^0 +10^y = 5

10^y = 4

y = log4/log10 = log4 = 0.6

Solution ( x,y) ---( 0, 0.6)

Solution lies on + ve y axis i.e. above x axis

OptionA