# Equivalent equations definition

Two systems of equations are equivalent if they have the same solution(s).

## How to find equivalent equation?

The first step is to know the rules of equivalent equations:

• Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation.
• Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
• Raising both sides of the equation to the same odd power or taking the same odd root will produce an equivalent equation.

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## Are these two equations equivalent?

Two equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2 x = 8 are equivalent equations, because when we solve each of them as follows, they have…

## What is the meaning of equivalent expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. To check whether a more complex expression is equivalent to a simpler expression:

## How do you do equivalent fractions and definition?

• Equivalent fractions may look different, but they have the same value.
• You can multiply or divide to find an equivalent fraction.
• Adding or subtracting does not work for finding an equivalent fraction.
• If you multiply or divide by the top of the fraction, you must do the same to the bottom.

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## What is equivalent equation?

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

## What is equivalent equation example?

For example, if we take 3x + 12 = 7x – 2 and subtract 3x from both sides and add 2 to both sides, we get 14 = 4x. In doing this, we haven’t changed the solution set, so 3x + 12 = 7x – 2 and 14 = 4x are equivalent equations.

## How do you solve an equivalent equation?

To solve equivalent equations, follow these five steps:Step 1 – Use the distributive property, if necessary.Step 2 – Combine like terms on the same side of the equal sign, if needed.Step 3 – Collect the variable being solved for on the same side of the equation.More items…•

## How do you know if an equation is equivalent or not?

0:561:51Determine if two equations are equivalent – YouTubeYouTubeStart of suggested clipEnd of suggested clipWe have the equations. 2x. Minus 5 equals 1 and 2 times X plus 2 equals 10 and the help out supposeMoreWe have the equations. 2x. Minus 5 equals 1 and 2 times X plus 2 equals 10 and the help out suppose that I give us the solution set of x equals 3 and say check to see if this is equivalent to both of

## What are equivalent functions?

Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.

## How do you equate two equations?

Suppose we have a pair of simultaneous equations, 2x − y = −2 and x + y = 5. We can solve these equations by taking the sum of the left hand sides and equating it to the sum of the right hand sides as follows: 2x − y + (x + y)=3x = 3. So, x = 1.

## How do you simplify equivalent expressions?

0:472:24Equivalent Expressions And Simplifying – YouTubeYouTubeStart of suggested clipEnd of suggested clipWe can combine this X – this X and this X. Which is a total of 3x. And we can combine 4 + 2 which isMoreWe can combine this X – this X and this X. Which is a total of 3x. And we can combine 4 + 2 which is a total of 6. And 3x plus 6 is not equal to 2x + 6 thereby eliminating choice C as well.

## How do you find an equivalent number?

To calculate the equivalent mass of a base, simply divide the molar mass of the base by the number of hydroxyl groups. Take, for example, calcium hydroxide Ca(OH)₂. A few simple calculations yield an equivalent of 37g/mol. To find the equivalent of an acid, divide the acid’s molar mass by the number of protons.

## How do you find the equivalent fraction?

For each fraction, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we have to find the third equivalent fraction of ⅔; then we have to multiply 2/3 by 3/3. Hence, 2/3 × (3/3) = 6/9, is the fraction equivalent to 2/3.

## How do you know if two equations are equivalent?

Two equations can be determined to be equivalent if they have the same solution. The two equations can also be determined to be equivalent if one…

## What does equivalent equation mean?

An equivalent equation means the equation has the same solution as another equation. The two equations do not have to look alike. Sometimes an eq…

## What are some examples of equivalent equations?

Some examples of equivalent equations in real-life could be adjusting a recipe to feed more people and comparing the prices of different weights of…

## What is equivalent equation?

Equivalent equations are two equations that have the same solution. They are used anytime multiple equations with the same variable need to equal each other, just like in our example.

## What is the point at which the value of the variable is equal in an equivalent equation?

Equivalent equations are two equations set equal to each other so that the variable has the same value in each equation. They are used to find break-even points. The break-even point is the point at which the value of the variable is equal in equivalent equations. For example, the selling point in which a company is selling their product for the same amount that it cost them to make it. This point is important to a company if they want to make a profit

## How to get the x on the same side of an equation?

Collect all the variables on the same side of the equal sign. Do this by adding or subtracting the variable with its coefficient from both sides of the equation. Add or subtract based on whichever is opposite of the current operation. By subtracting 7.50 x (subtracting is opposite of a positive 7.50 x ), we can move the x ‘s on the same side of the equation. What you do to one side of the equation you must do to the other side to keep the equation equal.

## What is the point at which the value of x is equal?

The point at which the value of x is equal is called the break-even point . Retail and product research and development departments use the break-even point to determine what price they would have to sell the product to break even and then add the percentage profit they want to make to the break-even price. Determining when two values are equal is very useful information.

## How many steps are needed to solve a multistep equation?

To solve any multi-step equation, you need to do a set of five steps in order. Not all problems will have all steps present, but you should check for them in order anyways.

## When to use break even method?

Remember to use this method anytime you have two equations that need to equal each other or to find break-even points for a product.

## Video Transcription

For example: Are the following equations, x = 7 and x + 2 = 9, equivalent? The solution: Our number 7 is the single possible solution of the equation x + 2 = 9.

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Then again, our equation x = 1 has just one single solution, and that is 1.

## What is equivalent equation?

Equivalent Equations. Equations, that have same roots are called equivalent. In particular, equations that don’t have roots are equivalent. Example 1. Equations. are equivalent, because each of them has unique root 5. Example 2. Equations. are equivalent, because they don’t have roots.

## Why aren’t equations equivalent?

are not equivalent, because first of them has two roots: 1 and -3, and another has one root: 2. Warning. Equations are equivalent only when they have exactly same roots. Example 4. Equations. are not equivalent, because, although 6 is root of both of them, but second equation also has another root: -6.

## What happens if both sides of an equation are non-negative?

If both sides of equation are non-negative, then raising both sides of equation to the same even power (or taking even root) will give equivalent equation. These rules give us an ability to “simplify” equations and even solve them. Example 1. Solve the equation. \$\$\$.

## What does raising both sides of an equation to the same odd power do?

Raising both sides of equation to the same odd power (or taking odd root) will give equivalent equation.

## What does “simplify” mean in math?

Usually, “simplify” means rewriting equation in such way that right side equals 0 .

## What does adding the same number do to the equation?

Adding (subtracting) same number (or expression) to both sides of the equation will give equivalent equation.

## How many sides can you add to an equation to get equivalent?

To obtain equivalent equation, we can add 8 to both sides of the equation:

## What is equivalent in math?

The term “equivalent” in math refers to two values, numbers or quantities which are the same.

## What are two mathematical expressions equivalent?

Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. For example, let’s solve the following numerical expressions: Thus, the above two expressions are equivalent and can be written as: 25 × 5 = 10 2 + 5 2. Similarly, following two math expressions are also equivalent:

## What is the equivalent symbol in a Venn diagram?

The use of the equivalent symbol (as three bars) is frequently used in Unicode programming for computers, as well as in Boolean algebra. Venn diagrams use the concept of logical equivalence to establish the relationship between two algebraic expressions and functions.

## Who invented the equal sign?

The sign “equals” (=) was invented by a Welsh mathematician Robert Recorde in 1557. Equivalent sign and equivalence of Boolean functions were explained by 19th century mathematician George Boole.

## Equivalent Definition

Equivalent: When two or more quantities have the same value. An equal sign is used to show that the quantities are the same value.

## What is equivalent?

The quantities can be represented by a number, fraction, decimal, or percentage. Equivalent does not always mean that the values look identical.

## Equivalent Numbers

Numbers can be used to represent values in different ways. The different representations are equivalent to each other. They look different but represent the same value. They can take on different forms and can be changed from one form to another. When the value changes, it is referred to it as converting.

## Equivalent Fractions

Fractions are equivalent to one another when they represent the same ratio or value. A fraction has a numerator and a denominator. The denominator describes the number of parts 1 whole has been split into. The numerator describes how many of those parts are being used.

## Equivalent Decimals

A decimal has a whole number part, which is written before the decimal point, and a ratio part, after the decimal point. It describes a portion of a full value. Each number after the decimal point shows a different portion of a whole number.

## Using Equivalent Math

Numbers can be converted from one form to another. Fractions can be changed to decimals, just as decimals can be changed to fractions. When numbers are converted from one form to another, they represent the same value and are equivalent. Numbers describe a value or a quantity. Equivalent forms are used to describe different things better.

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## What does “equivalent” mean in English?

Middle English, from Middle French or Late Latin; Middle French, from Late Latin aequivalent-, aequivalens, present participle of aequivalēre to have equal power, from Latin aequi- + valēre to be strong — more at wield. Keep scrolling for more. Keep scrolling for more.

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