Solve the following equation: 3 x +5 y =52 3 x −5 y =2

Add equations: Add the two equations to eliminate 5^y: 3^x + 5^y + 3^x - 5^y = 52 + 2, 2 * 3^x = 54, 3^x = 27. Solve for x: Solve for x: Since 3^3 = 27, x = 3. Substitute x: Substitute x = 3 into one of the original equations to find y: 3^3 + 5^y = 52, 27 + 5^y = 52, 5^y = 25. Solve for y: Solve for y: Since 5^2 = 25, y = 2.

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Solve the following equation: $\newline$ $3^x+5^y=52$ $\newline$ $3^x-5^y=2$

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Calculus

Find derivatives using the product rule II

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Q. Solve the following equation:

\newline

3^x+5^y=52

\newline

3^x-5^y=2

Add equations: Add the two equations to eliminate $5^y$ : $\newline$ $3^x + 5^y + 3^x - 5^y = 52 + 2,$ $\newline$ $2 \times 3^x = 54,$ $\newline$ $3^x = 27.$
Solve for x: Solve for x: $\newline$ Since $3^3 = 27$ , $\newline$ $x = 3$ .
Substitute $x$ : Substitute $x = 3$ into one of the original equations to find $y$ : $3^3 + 5^y = 52,$ $27 + 5^y = 52,$ $5^y = 25.$
Solve for y: Solve for y: $\newline$ Since $5^2 = 25$ , $\newline$ $y = 2$ .