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We speak of equivalent equations when we have two 2 equations that are having the same solution set.
Equivalent equations definition math. In mathematics an equivalence relation is a binary relation that is reflexive symmetric and transitive the relation is equal to is the canonical example of an equivalence relation where for any objects a b and c. For example let s solve the following numerical expressions. Our number 7 is the single possible solution of the equation x 2 9. 25 5 10 2 5 2.
Equations that have same roots are called equivalent. The most basic and common algebraic equations in math consist of one or more variables. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. 25 5 125.
In algebra an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. Sometimes a math equation contains fractions but requires decimals for the computation. Or the equation contains decimals but requires fractions. If a b then b a symmetric property and.
A a reflexive property. As a consequence of the reflexive. If a b and b c then a c transitive property. More about equivalent ratios equivalent ratios can be obtained by multiplying or dividing both sides by the same non zero number.
Equivalent equations are algebraic equations that have identical solutions or roots. Multiplying or dividing both sides of an equation by the same non zero number produces an equivalent equation. Equations x 2 7 and 2 x 1 11 are equivalent because each of them has unique root 5. Linear equations with one variable.
Are the equations x 7 and x 2 9 equivalent. Similarly the number 7 is the only solution to this equation. In particular equations that don t have roots are equivalent. Equivalent equations two equations whose solutions are the same.
Thus the above two expressions are equivalent and can be written as. Definition example. Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. Also 10 2 5 2 100 25 125.
1 dollar is equivalent to 100 cents 120 seconds.
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