# Which Equation is Equivalent to Another?

November 23, 2023
David Sunnyside

Whether you're comparing the prices of two shirts or trying to decide whether one company offers better customer service, knowing which equation is equivalent to another can be really helpful. Equivalent equations are systems of linear equations that have the same solution. You can tell which equations are equivalent by finding which values of the constant terms make both systems true. You can also check if the second equations are the same by checking which pair of values for the variable makes both systems true.

If you're trying to figure out which equation is equivalent to another, first try simplifying both sides of the equation by combining like terms and factoring. These steps can help you bring the variable to one side of the equation and the constant terms to the other. This will make the problem much easier to solve.

If your efforts are unsuccessful, you can try adding or subtracting the variables. These are not the only ways to find an equivalent equation, but they are very useful starting points.

Remember that if you add or subtract the same variable from both sides of an equation, it does not change the value of the sum. This is because addition is commutative, meaning it doesn't matter what order you put the terms in. This is why the equations 3a-8bequiv -3a-8b and 3a-8bequiv 3a-8b are considered to be equivalent. However, the two equations have different roots. So, if you're trying to figure out which of these is equal to which, be sure to take note of the root that each has.

David Sunnyside
Co-founder of Urban Splatter • Digital Marketer • Engineer • Meditator