Consider the following equation:
$4 x-y=6$
Step 1 of 2: Determine if the given ordered pair, $(-1,-10)$, satisfies the given equation.
Answer (1)
Substitute x = − 1 and y = − 10 into the equation 4 x − y = 6 .
Evaluate the left-hand side: 4 ( − 1 ) − ( − 10 ) = − 4 + 10 = 6 .
Since the left-hand side equals the right-hand side, the ordered pair satisfies the equation.
The ordered pair ( − 1 , − 10 ) satisfies the equation 4 x − y = 6 .
Explanation
Understanding the Problem We are given the equation 4 x − y = 6 and the ordered pair ( − 1 , − 10 ) . To determine if the ordered pair satisfies the equation, we need to substitute x = − 1 and y = − 10 into the equation and check if the equation holds true.
Substituting the Values Substitute x = − 1 and y = − 10 into the equation 4 x − y = 6 : 4 ( − 1 ) − ( − 10 ) = − 4 + 10 = 6 Since the left-hand side of the equation equals the right-hand side, the ordered pair satisfies the equation.
Conclusion Since 4 ( − 1 ) − ( − 10 ) = 6 , the ordered pair ( − 1 , − 10 ) satisfies the equation 4 x − y = 6 .
Examples
In real life, this type of problem can be used to check if a certain combination of resources meets a specific requirement. For example, if x represents the number of hours worked and y represents the amount of money spent on materials, the equation 4 x − y = 6 could represent a budget constraint. The ordered pair ( − 1 , − 10 ) would then represent a scenario where you worked -1 hours (which doesn't make sense in this context, but mathematically it can still be checked) and spent -$10 on materials (meaning you received $10). Checking if the ordered pair satisfies the equation helps determine if this scenario meets the budget constraint.
