Algebra

Solving the system of equations by adding them yields 2x = 14, so x = 7. Substituting x = 7 into the first equation gives y = 3, meaning the product xy is 21. Option A is incorrect because it likely results from an arithmetic error in solving for the individual variables.

To solve the equation 3^x = 27, recognize that 27 is equal to 3^3, thus x must be 3.. Since 27 equals 3³, the equation 3^x = 27 implies x = 3.

The correct answer is 3 because 27 is equal to 3^3. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !A common mistake is to confuse 3^2, which equals 9, with 3^3, which equals 27, leading to an incorrect solution. This highlights the importance of carefully evaluating the equation to determine the correct exponent.
• !Option A is incorrect because it likely results from an arithmetic error in solving for the individual variables.
• !Choice A 2 is a common trap from confusing 3² = 9 with 27, leading to an incorrect exponent.
• !Option B is incorrect because substituting x = -2 or x = -3 results in positive terms that sum to 20 or 30, not zero.
• !Option A is incorrect because 7 is simply the value of f(3), which neglects the outer function composition.

Answer each from memory — you'll see instantly whether you're right and why.

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