Solve the following equation. $6^x+6^y=42, x+y=3$.
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x=1,y=2
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x=1,y=1
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x=2,y= -1
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x=2,y=2
Reveal answer
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A
Correct answer
Explanation
Given 6^x + 6^y = 42 and x + y = 3. If x=1, y=2, then 6^1 + 6^2 = 6 + 36 = 42, which satisfies both equations.
AI explanation
Using the equation x + y = 3, we substitute y = 3 - x into the first equation to get 6^x + 6^(3 - x) = 42. Multiplying the entire equation by 6^x produces a quadratic equation (6^x)^2 - 42(6^x) + 216 = 0. Factoring this as (6^x - 6)(6^x - 36) = 0 gives the possible values for 6^x as 6 or 36. Therefore, x = 1 or x = 2, which correspondingly makes y = 2 or y = 1, confirming x = 1 and y = 2 as a valid pair.