Consider the following equation:
[tex]$4 x-4 y=8$[/tex]
Step 1 of 2: Determine the missing coordinate in the ordered pair (4, ?) so that it will satisfy the given equation.
Answer (2)
Substitute the given x -coordinate, x = 4 , into the equation 4 x − 4 y = 8 .
Simplify the equation to 16 − 4 y = 8 .
Solve for y by isolating the y term: − 4 y = − 8 .
Divide by -4 to find the y -coordinate: y = 2 , so the missing coordinate is 2 .
Explanation
Understanding the Problem We are given the equation 4 x − 4 y = 8 and the ordered pair ( 4 , ?) . We need to find the missing y -coordinate so that the ordered pair satisfies the equation.
Substituting the x-coordinate Substitute x = 4 into the equation 4 x − 4 y = 8 :
4 ( 4 ) − 4 y = 8
Simplifying the equation Simplify the equation: 16 − 4 y = 8
Isolating the y term Subtract 16 from both sides of the equation: − 4 y = 8 − 16 − 4 y = − 8
Solving for y Divide both sides by -4 to solve for y :
y = − 4 − 8 y = 2
Finding the missing coordinate Therefore, the missing coordinate is 2, and the ordered pair is ( 4 , 2 ) .
Examples
Understanding how to find missing coordinates in linear equations is crucial in various real-world applications. For instance, when designing a bridge, engineers use linear equations to ensure that the load is evenly distributed across the structure. By knowing one coordinate, they can determine the corresponding coordinate to maintain structural integrity. Similarly, in economics, linear equations help predict the relationship between supply and demand. Knowing one variable allows economists to calculate the other, aiding in decision-making and resource allocation. This concept is also vital in computer graphics for creating and manipulating images and animations.
By substituting the x-coordinate 4 into the equation 4 x − 4 y = 8 , we solve for the missing y-coordinate, which is 2. Thus, the ordered pair that satisfies the equation is (4, 2).
;
