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Vocabulary Activity
constraint
dimensional analysis
equation
equivalent equations
formula
1. A(n)
Use the words from the word bank to complete each sentence.
Some terms may be used more than once.
5. A(n)
6. A(n)
identity
literal equation
margin of error
multi-step equation
proportion
2. A formula or equation that involves several variables is a(n)
quantities.
3. A(n) equation is a mathematical statement that contains two expressions and an
equal sign.
sample
solution
solve an equation
survey
4. A statement that two ratios are equivalent is a(n) equivalent equation
is a condition that a solution must satisfy.
9. Salve an equation
statement.
is an equation that expresses a relationship between certain
is an equation that is true for every value of the variable.
7. An equation that uses more than one property of equality to solve it is a(n)
8. Equations that have the same solution are
• equivalent equation
to find all values of the variable that make the equation a true
10. The process of performing operations with units is called
Module 1 Review Writing and Solving Equations 61

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Systems of equation that have the same solution are called equivalent systems.

Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other.

Note: This idea of equivalent systems of equations pops up again in linear algebra. However, the examples and explanations in this article are geared to a high school algebra 1 class.

Example 1

We're given two systems of equations and asked if they're equivalent.

System A

−12x+9y=7

9x−12y=6

​

system B

−12x+9y=7

3x−4y=2

​

If we multiply the second equation in System B by 3, we get:

3x−4y=2

3(3x−4y)= 3(2)

9x−12y=6

​

Replacing the second equation of System B with this new equation, we get an equivalent system:

−12x+9y=7

9x−12y=6

​

Whoa! Look at that! This system is the same as System A, which means system A is equivalent to System B

To know more about Equations

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