Select the choice that represents this two-variable equation after it has been solved for $y$ in terms of $x$.
$2 x-y=7$
A. $y=5 x$
B. $y=2 x+7$
C. $x=\frac{y+7}{2}$
D. $y=2 x-7$
E. $y=14 x$
Answer (1)
Subtract 2 x from both sides of the equation: − y = 7 − 2 x .
Multiply both sides by − 1 : y = 2 x − 7 .
The equation solved for y in terms of x is y = 2 x − 7 .
Explanation
Understanding the Problem We are given the equation 2 x − y = 7 and asked to solve for y in terms of x . This means we want to isolate y on one side of the equation.
Isolating y To isolate y , we first subtract 2 x from both sides of the equation: 2 x − y − 2 x = 7 − 2 x − y = 7 − 2 x
Solving for y Next, we multiply both sides of the equation by − 1 to solve for y :
( − 1 ) ( − y ) = ( − 1 ) ( 7 − 2 x ) y = − 7 + 2 x y = 2 x − 7
Final Answer Therefore, the equation solved for y in terms of x is y = 2 x − 7 .
Examples
Understanding how to rearrange equations to solve for a specific variable is a fundamental skill in algebra and has many practical applications. For example, in physics, you might have an equation that relates distance, speed, and time, and you need to solve for time in terms of distance and speed. Similarly, in economics, you might have an equation that relates cost, price, and quantity, and you need to solve for quantity in terms of cost and price. These skills are essential for problem-solving in various fields.
