2 Decide Whether an Ordered Pair Is a Solution of an Equation EXAMPLE 2 Determine whether each ordered pair is a solution of 4x 5y 11. a) (1, 3) b) a3 2 , 5b Solution a) Solutions to the equation 4x 5y 11 are written in the form (x, y) where (x, y) is called an ordered pair. Therefore, the ordered pair (1, 3) means that x 1 and y 3. (1, 3) Q a x-coordinate y-coordinate To determine whether (1, 3) is a solution of 4x 5y 11, we substitute 1 for x and 3 for y. Remember to put these values in parentheses. 4x 5y 11 4(1) 5(3) 11 Substitute x 1 and y 3. 4 15 11 Multiply. 11 11 True Since substituting x 1 and y 3 into the equation gives the true statement 11 11, (1, 3) is a solution of 4x 5y 11. We say that (1, 3) satisfi es 4x 5y 11. b) The ordered pair a3 2 , 5b tells us that x 3 2 and y 5. 4x 5y 11 4 a3 2 b 5(5) 11 Substitute 3 2 for x and 5 for y. 6 25 11 Multiply. 31 11 False Since substituting a3 2 , 5b into the equation gives the false statement 31 11, the ordered pair is not a solution to the equation. Make sure you are substituting the variable x with the first quantity in the given ordered pair and the variable y with the second quantity of the ordered pair. YOU TRY 2 Determine whether each ordered pair is a solution of the equation y 3 4 x 5. a) (12, 4) b) (0, 7) c) (8, 11) If the variables in the equation are not x and y, then the variables in the ordered pairs are written in alphabetical order. For example, solutions to 2a b 7 are ordered pairs of the form (a, b). 142 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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