$5x - 2y = 5$
Step 1 of 2: Determine if the given ordered pair $(-3, \frac{5}{2})$ satisfies the given equation.
Answer (1)
Substitute x = − 3 and y = 2 5 into the equation 5 x − 2 y = 5 .
Evaluate the left-hand side: 5 ( − 3 ) − 2 ( 2 5 ) = − 15 − 5 = − 20 .
Compare the result with the right-hand side: − 20 = 5 .
The ordered pair does not satisfy the equation: F a l se .
Explanation
Understanding the Problem We are given the equation 5 x − 2 y = 5 and the ordered pair ( − 3 , 2 5 ) . We need to determine if this ordered pair satisfies the equation. This means we need to substitute x = − 3 and y = 2 5 into the equation and see if the left-hand side equals the right-hand side.
Substitution and Evaluation Substitute x = − 3 and y = 2 5 into the equation 5 x − 2 y = 5 . We get: 5 ( − 3 ) − 2 ( 2 5 ) = − 15 − 5 = − 20
Comparison and Conclusion Now we compare the result, − 20 , with the right-hand side of the equation, which is 5 . Since − 20 = 5 , the ordered pair ( − 3 , 2 5 ) does not satisfy the equation 5 x − 2 y = 5 .
Examples
In real life, this type of problem can be used to check if a point lies on a line. For example, if you have a budget constraint represented by a linear equation, you can check if a certain combination of goods (represented by an ordered pair) is within your budget. If the ordered pair satisfies the equation, it means that the combination of goods exactly uses up your budget. If it doesn't, it means you either have money left over or you're over budget.
