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1
**4.4 Equations as Relations**

The equation p = 0.69d is an example of an equation in two variables. A solution of an equation in two variables is an ordered pair that results in a true statement when substituted into the equation.

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**Solve Using a Replacement Set**

Find the solution set for y = 2x + 3, given the replacement set {(-2 , -1) , (-1 , 3), (0 , 4), (3 , 9)}. Make a table. Substitute each ordered pair into the equation. The ordered pairs (-2 , -1) and (3 , 9) result in true statements. The solution set is {(-2 , -1) , (3 , 9)}.

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**Solve Using a Given Domain**

Solve b = a + 5 if the domain is {-3 , -1, 0 , 2 , 4}. Make a table. The values of a come from the domain. Substitute each value of a into the equation to determine the values of b in the range. The solution set is {(-3 , 2) , (-1 , 4) , (0 , 5), (2 , 7) , (4 , 9)}

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Graph Solution Sets You can graph the ordered pairs in the solution set for an equation in two variables. The domain contains values represented by the independent variable. The range contains the corresponding value represented by the dependent variable.

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**Solve and Graph the Solution Set**

Solve 4x + 2y = 10 if the domain is {-1 , 0 , 2 , 4}. Graph the solution set. First solve the equation for y in terms of x. This makes creating a table of values easier.

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**Solve and Graph the Solution Set**

Substitute each value of x from the domain to determine the corresponding values of y in the range. Then, graph the solution set.

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**Solve for a Dependent Variable**

See example 4 on p. 213.

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