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solve the followimg equation 3x+5y=523^x+5^y=52, 3x−5y=23^x-5^y=2

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Full solution

Q. solve the followimg equation 3x+5y=523^x+5^y=52, 3x−5y=23^x-5^y=2
  1. Add equations: Add the two equations to eliminate 5y5^y: \newline3x+5y+3x−5y=52+2,3^x + 5^y + 3^x - 5^y = 52 + 2,\newline2×3x=54,2 \times 3^x = 54,\newline3x=27.3^x = 27.
  2. Solve for x: Solve for x:\newlineSince 33=273^3 = 27,\newlinex=3x = 3.
  3. Substitute xx: Substitute x=3x = 3 into one of the original equations to find yy:33+5y=52,3^3 + 5^y = 52,27+5y=52,27 + 5^y = 52,5y=25.5^y = 25.
  4. Solve for y: Solve for y:\newlineSince 52=255^2 = 25,\newliney=2y = 2.

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