Consider the following equation:
[tex]4 x+y=1[/tex]
Determine if the given ordered pair [tex](1,-3)[/tex] satisfies the given equation.
Answer (2)
Substitute the given values x = 1 and y = − 3 into the equation 4 x + y = 1 .
Simplify the expression: 4 ( 1 ) + ( − 3 ) = 4 − 3 = 1 .
Check if the left-hand side equals the right-hand side: 1 = 1 .
Since the equation holds true, the ordered pair ( 1 , − 3 ) satisfies the equation. Yes
Explanation
Understanding the Problem We are given the equation 4 x + y = 1 and the ordered pair ( 1 , − 3 ) . To determine if the ordered pair satisfies the equation, we need to substitute the x and y values from the ordered pair into the equation and check if the equation holds true.
Substitution Substitute x = 1 and y = − 3 into the equation 4 x + y = 1 . This gives us: 4 ( 1 ) + ( − 3 ) = 1
Simplification Now, we simplify the left-hand side of the equation: 4 ( 1 ) + ( − 3 ) = 4 − 3 = 1
Conclusion Since the left-hand side of the equation equals the right-hand side (i.e., 1 = 1 ), the ordered pair ( 1 , − 3 ) satisfies the equation 4 x + y = 1 .
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 use this method to determine if a particular combination of goods (represented as an ordered pair) is within your budget.
The ordered pair ( 1 , − 3 ) satisfies the equation 4 x + y = 1 because substituting the values leads to a true statement. After substitution and simplification, both sides of the equation equal 1. Therefore, the answer is yes.
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