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Published byGrant Harber Modified over 3 years ago

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**Ordered pairs ( x , y ) as solutions to Linear Equations**

Here are some examples of Linear Equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations.

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**Ordered pairs ( x , y ) as solutions to Linear Equations**

Here are some examples of Linear equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations. Every solution of a Linear equation is an ordered pair of numbers, x and y. This pair, when substituted into the equation, creates an equality. If no equality exists, the ordered pair IS NOT a solution.

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**STEPS : 1. Substitute the given ( x , y ) into the equation.**

Ordered pairs ( x , y ) as solutions to Linear Equations Here are some examples of Linear equations. The variables have ones as their exponents. They create lines that contain many ( x , y ) points that satisfy the given equations. Every solution of a Linear equation is an ordered pair of numbers, x and y. This pair, when substituted into the equation creates an equality. If no equality exists, the ordered pair IS NOT a solution. STEPS : 1. Substitute the given ( x , y ) into the equation. 2. Check to see if an equality exists.

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**Substitute x = 2, and y =3 into the equation.**

EXAMPLE : Substitute x = 2, and y =3 into the equation.

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**Substitute x = 2 , and y = 3 into the equation.**

EXAMPLE : Substitute x = 2 , and y = 3 into the equation.

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**Substitute x = 2 , and y = 3 into the equation.**

EXAMPLE : Substitute x = 2 , and y = 3 into the equation. Since this creates an equality, the given point IS a solution to the equation.

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EXAMPLE :

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EXAMPLE : Substitute x = , and y = 7 into the equation.

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EXAMPLE : Substitute x = , and y = 7 into the equation. Since the equality doesn’t exist, the given ordered pair IS NOT a solution to the equation.

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**You try one. See if you can get the solution first without seeing how I did it.**

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**You try one. See if you can get the solution first without seeing how I did it.**

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**You try one. See if you can get the solution first without seeing how I did it.**

Substitute x = 3 and y = 9 into the equation

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**You try one. See if you can get the solution first without seeing how I did it.**

Substitute x = 3 and y = 9 into the equation Since an equality exists, the ordered pair IS a solution to the equation.

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PRACTICE Complete the following problems. You can check your answers in the solution bank. Test each ordered pair and see if it is a solution to the given equation.

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PRACTICE Complete the following problems. You can check your answers in the solution bank. Test each ordered pair and see if it is a solution to the given equation.

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1 Section 5.3 Linear Systems of Equations. 2 THREE EQUATIONS WITH THREE VARIABLES Consider the linear system of three equations below with three unknowns.

1 Section 5.3 Linear Systems of Equations. 2 THREE EQUATIONS WITH THREE VARIABLES Consider the linear system of three equations below with three unknowns.

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