\frac{13 y}{13}=\frac{30 y}{13}
Answer (1)
Simplify the left side of the equation: y = 13 30 y .
Multiply both sides by 13: 13 y = 30 y .
Subtract 13 y from both sides: 0 = 17 y .
Divide by 17 to find the solution: y = 0 .
Explanation
Understanding the equation We are given the equation 13 13 y = 13 30 y . Our goal is to solve for y .
Simplifying the left side First, simplify the left side of the equation: 13 13 y = 1 ⋅ y = y . So the equation becomes y = 13 30 y .
Eliminating the fraction Now, we want to isolate y . Multiply both sides of the equation by 13 to eliminate the fraction: 13 ⋅ y = 13 ⋅ 13 30 y , which simplifies to 13 y = 30 y .
Isolating y Next, subtract 13 y from both sides of the equation to get all the y terms on one side: 13 y − 13 y = 30 y − 13 y , which simplifies to 0 = 17 y .
Solving for y Finally, divide both sides by 17 to solve for y : 17 0 = 17 17 y , which simplifies to 0 = y . Therefore, y = 0 .
Verifying the solution To verify the solution, substitute y = 0 back into the original equation: 13 13 ( 0 ) = 13 30 ( 0 ) , which simplifies to 0 = 0 . This confirms that our solution is correct.
Examples
In physics, when analyzing forces in equilibrium, you might encounter equations similar to the one we solved. For example, if the sum of forces acting on an object in one direction is represented by 13 13 y and the sum of forces in the opposite direction is 13 30 y , setting these equal helps determine the equilibrium condition. Solving for y in such a scenario can tell you about the magnitude of a related physical quantity when the system is balanced. This principle is crucial in structural engineering and mechanics to ensure stability.
