What Is an Equivalent Equation?

Author Edith Carli

Posted Jul 12, 2022

Reads 120

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An equivalent equation is an equation that is mathematically equivalent to another equation. In other words, two equations are equivalent if they have the same solutions.

There are many methods for determining whether two equations are equivalent. One method is to graph the equations and see if they produce the same graph. If the two equations are equivalent, then they will have the same slope and y-intercept.

Another method for determining equivalency is to solve both equations for the same variable. If the equations are equivalent, then they will have the same solution.

yet another method is to change the coefficients of the variables in one equation so that it matches the other equation. If the equations are equivalent, then they will have the same solutions.

For example, consider the following two equations:

y = 2x + 3 y = -x + 5

These equations are equivalent because they have the same slope and y-intercept. Additionally, if we solve each equation for y, we get:

y = 2x + 3 y = -x + 5

And if we solve each equation for x, we get:

x = (y-3)/2 x = (y-5)/(-1)

So, the solutions of each equation are the same. Finally, if we change the coefficients of the variables in one equation, we get:

2y = 4x + 6 -y = -x + 5

Which are still equivalent because they have the same solutions.

In conclusion, there are many ways to determine whether two equations are equivalent. Two equations are equivalent if they have the same solutions.

What is an equation solved for y2?

An equation is a mathematical statement that two things are equal. In solving an equation, we find the value of the variable that makes the equation true. For example, in the equation 2x + 3 = 5, we are solving for x, so we find the value of x that makes the equation true.

In the equation y2 + 2y = 5, we are solving for y2. We do this by finding the value of y that makes the equation true and then squaring it. So, in this equation, we are looking for the value of y that when added to itself and then 2 times y equals 5. This value can be found by using the Quadratic Formula. The Quadratic Formula is:

y = (-b ± √(b2 - 4ac)) / 2a

In this equation, a is equal to 1, b is equal to 2, and c is equal to -3. So, we plug those values into the Quadratic Formula and solve for y.

y = (-2 ± √(4 - 4(-3))) / 2(1)

y = (-2 ± √(16 + 12)) / 2(1)

y = (-2 ± √(28)) / 2

y = (-2 ± √(28)) / 2

y = (-2 ± √(784)) / 2

y = (-2 ± 28) / 2

y = (-30 ± 28) / 2

y = (-30 / 2) ± (28 / 2)

y = -15 ± 14

y = -15 + 14

y = -1

y = 1

So, the two values for y that make the equation true are -1 and 1. Now, we square each of these values to solve for y2.

(-1)2 = 1

12 = 1

So, the equation y2 + 2y = 5 is true when y is equal to -1 or 1 and y2 is equal to 1.

Frequently Asked Questions

How do you find the equivalent of an equation?

To find an equivalent equation, you need to first understand the properties of Equations and what general types of equations there are. There are three main types of equations: Linear Equations, Nonlinear Equations, and Functional Equations. Linear equations are easiest to solve and can be written in two basic forms: a linear equation in one variable and a linear equation in multiple variables. Nonlinear equations can be much more complicated and often involve function plotting or parametric analysis. Functional equations are used to describe relationships between two or more systems or reactions. Once you understand these basics, you can use them to solve equations using various methods.

What is the difference between two equations that are not equivalent?

Different values will be obtained if the equations are not equivalent.

What are equivalent expressions?

Two algebraic expressions are equivalent if and only if the two expressions have the same value when we substitute the same value for the variable (s).

Are the equations x = 7 and x + 2 = 9 equivalent?

The equations x = 7 and x + 2 = 9 are equivalent because they have the same solution set: x = 7 and x + 2 = 9.

How do you know if an equation is equivalent?

If the equation has the same variables on both sides, then it is equivalent.

Edith Carli

Edith Carli

Writer at CGAA

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Edith Carli is a passionate and knowledgeable article author with over 10 years of experience. She has a degree in English Literature from the University of California, Berkeley and her work has been featured in reputable publications such as The Huffington Post and Slate. Her focus areas include education, technology, food culture, travel, and lifestyle with an emphasis on how to get the most out of modern life.

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