$4 x-y=5$
Determine the missing coordinate in the ordered pair $\left(?, \frac{3}{2}\right)$ so that it will satisfy the given equation.
Answer (2)
Substitute y = 2 3 into the equation 4 x − y = 5 .
Solve for x in the equation 4 x − 2 3 = 5 .
Add 2 3 to both sides: 4 x = 2 13 .
Divide by 4: x = 8 13 . The missing coordinate is 8 13 .
Explanation
Understanding the Problem We are given the equation 4 x − y = 5 and the ordered pair ( ? , 2 3 ) . Our goal is to find the x -coordinate that satisfies the equation when y = 2 3 .
Substituting the Value of y Substitute y = 2 3 into the equation 4 x − y = 5 :
4 x − 2 3 = 5
Isolating the x term Add 2 3 to both sides of the equation: 4 x = 5 + 2 3 4 x = 2 10 + 2 3 4 x = 2 13
Solving for x Divide both sides by 4 to solve for x :
x = 4 2 13 x = 2 13 × 4 1 x = 8 13
Final Answer Therefore, the missing coordinate is 8 13 .
Examples
In real-world scenarios, this type of problem can be applied to various situations. For example, imagine a simple linear relationship between the number of hours worked and the amount earned. If the equation is 4 x − y = 5 , where x represents hours worked and y represents the base pay, finding the missing coordinate helps determine how many hours someone needs to work to earn a specific amount above the base pay. If the base pay is 2 3 dollars, we can calculate the hours needed to satisfy the equation.
The missing coordinate that satisfies the equation 4 x − y = 5 for the ordered pair ( ? , 2 3 ) is 8 13 . Thus, the complete ordered pair is ( 8 13 , 2 3 ) .
;
