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Davi da Silva
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i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
Davi da Silva said:i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
It means "if and only if". I.E. logical equivalence. The expression on the left is true if the expression on the right is true, and the expression on the left is true only if the expression on the right is true.Davi da Silva said:i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
In this particular example, if x+ 5= y+ 2 then subtracting 2 from both sides, x+ 3= y. Conversely, if x+ 3= y then adding 2 to both sides gives x+ 5= y+ 2. That is, if x+ 5= y+ 2 is true, then so is x+ 3= y and, conversely, if x+ 3= y is true then so is x+ 5= y+ 2. Each side implies the other.Davi da Silva said:i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
That was IFF on my analysis course. Is that not used any more?DaleSpam said:It means "if and only if". I.E. logical equivalence.
HallsofIvy said:Just a slight addition: "y= 3=> y^2= 9" but it is NOT true that "y= 3 <=> y^2= 9" because it is not true that "y^2= 9=> y= 3". If y^2= 9 y itself may be 3 or -3.
I think both are used. It just depends on a particular authors preferences.sophiecentaur said:That was IFF on my analysis course. Is that not used any more?
IFF you say so!DaleSpam said:I think both are used. It just depends on a particular authors preferences.
To solve equations with two variables, you need to isolate one variable on one side of the equation by using algebraic operations like addition, subtraction, multiplication, and division. In this case, you can start by subtracting x from both sides of the first equation, and then subtracting y from both sides of the second equation. This will give you two equations with only one variable on each side.
The variables x and y represent the unknown quantities in the equations. They can take on any value that makes the equations true. By solving for their values, you can find the solution to the equations and determine the relationship between x and y.
No, algebraic operations are necessary to solve equations with multiple variables. These operations allow you to manipulate the equations and isolate the variables, making it easier to find their values. Other methods, such as graphing or using a calculator, may help in visualizing the solutions but they ultimately rely on algebraic principles.
To check if you have the correct solution, you can substitute the values of x and y into the original equations and see if they make the equations true. For example, if x = 1 and y = 3, then the first equation becomes 1 + 5 = 3 + 2, which is true. You can also graph the equations and see if the coordinates of the solution point satisfy both equations.
Some common mistakes to avoid include not distributing numbers correctly, mixing up signs (+ and -), and not keeping track of the operations you perform on both sides of the equations. It's also important to double check your solution and make sure it satisfies both equations and follows any given restrictions, if applicable.