Consider the following equation:
[tex]$4 x+y=1$[/tex]
Determine if the given ordered pair, $(-1,5)$, satisfies the given equation.
Answer (2)
Substitute x = − 1 and y = 5 into the equation 4 x + y = 1 .
Evaluate the expression: 4 ( − 1 ) + 5 = − 4 + 5 = 1 .
Since 1 = 1 , the ordered pair satisfies the equation.
The ordered pair ( − 1 , 5 ) satisfies the equation 4 x + y = 1 , so the answer is T r u e .
Explanation
Understanding the problem We are given the equation 4 x + y = 1 and the ordered pair ( − 1 , 5 ) . To determine if the ordered pair satisfies the equation, we need to substitute x = − 1 and y = 5 into the equation and check if the equation holds true.
Substituting the values Substitute x = − 1 and y = 5 into the equation 4 x + y = 1 :
4 ( − 1 ) + 5 = − 4 + 5 = 1
Checking the equality Since the left-hand side of the equation equals the right-hand side, the ordered pair ( − 1 , 5 ) satisfies the equation 4 x + y = 1 .
Conclusion Therefore, the ordered pair ( − 1 , 5 ) satisfies the given equation.
Examples
In real life, this concept is used to check if a particular solution works for a given constraint. For example, in budgeting, you might have an equation representing your total expenses based on the number of items you buy. If you have a certain amount of money, you can check if buying a specific number of each item fits within your budget by substituting the quantities into the equation. If the equation holds true, then that combination of items is a feasible solution.
The ordered pair ( − 1 , 5 ) satisfies the equation 4 x + y = 1 because substituting the values results in a true statement, 1 = 1 . Therefore, the answer is True .
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