Consider the following equation:
[tex]4 x-y=6[/tex]
Step 2 of 2: Determine if the given ordered pair, [tex](3.3,-1)[/tex], satisfies the given equation.
Answer (2)
The ordered pair (3.3, -1) does not satisfy the equation 4x - y = 6 because substituting the values results in 14.2, which is not equal to 6. Therefore, the answer is no.
;
Substitute x = 3.3 and y = − 1 into the equation 4 x − y = 6 .
Calculate 4 ( 3.3 ) − ( − 1 ) = 13.2 + 1 = 14.2 .
Check if 14.2 = 6 . Since it's not, the ordered pair does not satisfy the equation.
The ordered pair ( 3.3 , − 1 ) does not satisfy the equation 4 x − y = 6 .
No
Explanation
Understanding the Problem We are given the equation 4 x − y = 6 and the ordered pair ( 3.3 , − 1 ) . To determine if the ordered pair satisfies the equation, we need to substitute x = 3.3 and y = − 1 into the equation and check if the equation holds true.
Substituting the Values Substitute x = 3.3 and y = − 1 into the equation 4 x − y = 6 :
4 ( 3.3 ) − ( − 1 ) = 13.2 + 1 = 14.2
Checking the Result Now, we check if the result is equal to 6. Since 14.2 e q 6 , the ordered pair ( 3.3 , − 1 ) does not satisfy the equation 4 x − y = 6 .
Final Answer Therefore, the ordered pair ( 3.3 , − 1 ) does not satisfy the given equation 4 x − y = 6 .
Examples
In real life, linear equations can model relationships between variables, such as the cost of items and the quantity purchased. For example, if a taxi service charges a fixed fee plus a per-mile rate, the equation can help determine if a particular fare is consistent with the distance traveled. Checking if an ordered pair satisfies the equation is like verifying if a specific scenario fits the established relationship. This is useful in budgeting, financial planning, and many other practical applications where understanding linear relationships is crucial.
