Determine whether a Number is a systems of an Equation

Solving an equation is like finding out the answer come a puzzle. An algebraic equation claims that two algebraic expressions space equal. To deal with an equation is to recognize the values of the variable that make the equation a true statement. Any kind of number that renders the equation true is referred to as a systems of the equation. That is the answer come the puzzle!


Solution of one Equation

A solution to one equation is a worth of a variable that makes a true statement when substituted into the equation.The process of finding the solution to one equation is referred to as solving the equation.

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To find the solution to an equation means to uncover the value of the change that makes the equation true. Can you acknowledge the solution of x+2=7? If you stated 5, she right! us say 5 is a solution to the equation x+2=7 because when us substitute 5 because that x the result statement is true.

eginarray\ hfill x+2=7hfill \ hfill 5+2stackrel?=7hfill \ \ hfill 7=7quadcheckmark hfill endarray

Since 5+2=7 is a true statement, we understand that 5 is without doubt a systems to the equation.The symbol stackrel?= asks even if it is the left next of the equation is same to the best side. Once we know, we can readjust to an equal authorize ext(=) or not-equal authorize ext( ot = ).


Determine whether a number is a solution to one equation.

Substitute the number because that the variable in the equation.Simplify the expression on both sides of the equation.Determine even if it is the resulting equation is true.If that is true, the number is a solution.If it is not true, the number is not a solution.

example

Determine even if it is x=5 is a systems of 6x - 17=16.

Solution

6x-17=16
Substitute colorred5 for x.6cdotcolorred5-17=16
Multiply.30-17=16
Subtract.13=16

So x=5 is no a solution to the equation 6x - 17=16.


try it


example

Determine even if it is y=2 is a equipment of 6y - 4=5y - 2.


Show Solution

SolutionHere, the variable shows up on both political parties of the equation. We must substitute 2 because that each y.

6y-4=5y-2
Substitute colorred2 because that y.6(colorred2)-4=5(colorred2)-2
Multiply.12-4=10-2
Subtract.8=8

Since y=2 results in a true equation, we know that 2 is a systems to the equation 6y - 4=5y - 2.

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In the following video we show much more examples of how to verify even if it is an integer is a equipment to a direct equation.