Consider the following equation:
[tex]$4 x+4 y=13$[/tex]
Step 1 of 2: Determine if the given ordered pair, (-1,-3), satisfies the given equation.
Answer (1)
Substitute x = − 1 and y = − 3 into the equation 4 x + 4 y = 13 .
Evaluate the left-hand side: 4 ( − 1 ) + 4 ( − 3 ) = − 4 − 12 = − 16 .
Compare the result with the right-hand side: − 16 e q 13 .
Conclude that the ordered pair ( − 1 , − 3 ) does not satisfy the equation. F a l se
Explanation
Understanding the problem We are given the equation 4 x + 4 y = 13 and the ordered pair ( − 1 , − 3 ) . To determine if the ordered pair satisfies the equation, we need to substitute x = − 1 and y = − 3 into the equation and check if the equation holds true.
Substitution Substitute x = − 1 and y = − 3 into the equation 4 x + 4 y = 13 :
4 ( − 1 ) + 4 ( − 3 ) = 13
Evaluation Evaluate the left-hand side of the equation: 4 ( − 1 ) + 4 ( − 3 ) = − 4 − 12 = − 16
Comparison Compare the result with the right-hand side of the equation. We have − 16 on the left-hand side and 13 on the right-hand side. Since − 16 e q 13 , the ordered pair ( − 1 , − 3 ) does not satisfy the equation 4 x + 4 y = 13 .
Conclusion Therefore, the ordered pair ( − 1 , − 3 ) does not satisfy the given equation 4 x + 4 y = 13 .
Examples
In real life, this type of problem can be used to check if a certain combination of items satisfies a budget constraint. For example, if x represents the number of apples and y represents the number of bananas, and the equation represents the total cost constraint, we can use this method to check if buying -1 apples and -3 bananas would satisfy the budget. Although negative quantities don't make sense in this context, the mathematical principle applies to scenarios with valid quantities.
