## Determine Whether a Number is a Systems of an Equation

Solving an equation is choose finding out the answer to a puzzle. An algebraic equation claims that two algebraic expressions are equal. To solve an equation is to recognize the worths of the variable that make the equation a true statement. Any number that renders the equation true is called a solution of the equation. It is the answer to the puzzle!

### Solution of an Equation

A solution to an equation is a value of a variable that renders a true statement as soon as substituted into the equation.The process of finding the solution to an equation is called resolving the equation.

You are watching: A value that makes an equation true

To discover the solution to an equation means to uncover the value of the variable that renders the equation true. Can you identify the solution of x+2=7? If you shelp 5, you’re right! We say 5 is a solution to the equation x+2=7 because as soon as we substitute 5 for x the resulting statement is true.

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

Because 5+2=7 is a true statement, we know that 5 is indeed a solution to the equation.The symbol stackrel?= asks whether the left side of the equation is equal to the best side. Once we understand, we deserve to adjust to an equal sign ext(=) or not-equal sign ext( ot = ).

### Determine whether a number is a solution to an equation.

Substitute the number for the variable in the equation.Simplify the expressions on both sides of the equation.Determine whether the resulting equation is true.If it is true, the number is a solution.If it is not true, the number is not a solution.

### example

Determine whether x=5 is a solution 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 not a solution to the equation 6x - 17=16.

### example

Determine whether y=2 is a solution of 6y - 4=5y - 2.

Sexactly how Solution

SolutionHere, the variable shows up on both sides of the equation. We have to substitute 2 for each y.

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

Due to the fact that y=2 outcomes in a true equation, we understand that 2 is a solution to the equation 6y - 4=5y - 2.

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In the adhering to video we present even more examples of how to verify whether an integer is a solution to a straight equation.