Solve the literal equation for $y$. Simplify your answer.
$\frac{1}{y}=\frac{1}{z}$
Answer (2)
Take the reciprocal of both sides of the equation y 1 = z 1 .
Simplify to find the value of y .
The solution is y = z .
Therefore, the final answer is y = z .
Explanation
Understanding the equation We are given the equation y 1 = z 1 and we want to solve for y .
Taking reciprocals To solve for y , we can take the reciprocal of both sides of the equation. The reciprocal of y 1 is y , and the reciprocal of z 1 is z .
Solution Therefore, we have y = z .
Examples
In physics, if you have two resistors in parallel with the same resistance y and z , and you know that the total resistance R t o t a l 1 = y 1 + z 1 , then solving the equation y 1 = z 1 tells you that the resistances are equal, i.e., y = z . This helps in simplifying circuit calculations and understanding the properties of parallel resistors.
To solve the equation y 1 = z 1 , we take the reciprocals of both sides, leading to the solution y = z . This means that the two variables are equal. Hence, the final simplified answer is y = z .
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