Complete the ordered pair so that it is a solution of the given linear equation.
[tex]2 x+y=-8[/tex]
Answer (1)
Substitute each ordered pair (x, y) into the equation 2 x + y = − 8 .
Check if the equation holds true for each ordered pair.
Option A: ( − 5 , 2 ) , ( 0 , − 8 ) , ( 1 , − 10 ) all satisfy the equation.
The correct answer is ( − 5 , 2 ) , ( 0 , − 8 ) , ( 1 , − 10 ) .
Explanation
Understanding the Problem We are given the equation 2 x + y = − 8 and four sets of ordered pairs. Our goal is to determine which set contains only ordered pairs that are solutions to the equation. To do this, we will substitute the x and y values from each ordered pair into the equation and check if the equation holds true.
Testing Option A Let's test the ordered pairs in option (A): ( − 5 , 2 ) , ( 0 , − 8 ) , ( 1 , − 10 ) .
For ( − 5 , 2 ) : 2 ( − 5 ) + 2 = − 10 + 2 = − 8 . This is true. For ( 0 , − 8 ) : 2 ( 0 ) + ( − 8 ) = 0 − 8 = − 8 . This is true. For ( 1 , − 10 ) : 2 ( 1 ) + ( − 10 ) = 2 − 10 = − 8 . This is true.
Since all ordered pairs in option (A) satisfy the equation, this is our solution.
Checking Other Options Let's quickly check the other options to confirm that they are incorrect.
Option (B): ( − 5 , 2 ) , ( 0 , − 12 ) , ( 1 , − 10 ) For ( 0 , − 12 ) : 2 ( 0 ) + ( − 12 ) = − 12 e q − 8 . This is false.
Option (C): ( − 5 , − 5 ) , ( 0 , − 8 ) , ( 1 , − 10 ) For ( − 5 , − 5 ) : 2 ( − 5 ) + ( − 5 ) = − 10 − 5 = − 15 e q − 8 . This is false.
Option (D): ( − 5 , 2 ) , ( 0 , 0 ) , ( 1 , − 10 ) For ( 0 , 0 ) : 2 ( 0 ) + 0 = 0 e q − 8 . This is false.
Final Answer Therefore, the correct set of ordered pairs that satisfy the equation 2 x + y = − 8 is option (A): ( − 5 , 2 ) , ( 0 , − 8 ) , ( 1 , − 10 ) .
Examples
Linear equations are used in many real-world applications, such as determining the cost of items. For example, if a store sells apples for $2 each and you have a coupon for $8 off your total purchase, the equation 2x + y = -8 can represent the relationship between the number of apples you buy (x) and the amount you still owe (y, which would be negative since you have a coupon). If you buy 5 apples, you owe $2(5) - 8 = $2. If you buy 0 apples, you 'owe' -$8 (the value of your coupon). If you buy 1 apple, you owe $2(1) - 8 = -$6.
