Solve for $y$. -6x + 2y = 8 y=[?]x+\square
Answer (2)
Add 6 x to both sides of the equation: 2 y = 6 x + 8 .
Divide both sides by 2: y = 3 x + 4 .
The equation is now in the form y = [ ?] x + □ .
The solution is y = 3 x + 4 .
Explanation
Understanding the Problem We are given the equation − 6 x + 2 y = 8 and asked to solve for y and express it in the form y = [ ?] x + □ . This means we need to isolate y on one side of the equation.
Isolating the y term First, we add 6 x to both sides of the equation to isolate the term with y :
− 6 x + 2 y + 6 x = 8 + 6 x 2 y = 6 x + 8
Solving for y Next, we divide both sides of the equation by 2 to solve for y :
2 2 y = 2 6 x + 8 y = 2 6 x + 2 8 y = 3 x + 4
Final Answer Therefore, the equation is now in the form y = [ ?] x + □ , where the coefficient of x is 3 and the constant term is 4.
Examples
Understanding how to isolate variables in linear equations is a fundamental skill in algebra and is used extensively in various fields. For example, in physics, you might need to rearrange an equation to solve for velocity given distance and time. Similarly, in economics, you might rearrange a supply and demand equation to determine the equilibrium price. This skill is also crucial in computer science for manipulating data and creating algorithms.
The solution to the equation − 6 x + 2 y = 8 is y = 3 x + 4 after isolating y by adding 6 x and dividing by 2. The equation is now in the form y = [ ?] x + □ , where the coefficient is 3 and the constant is 4.
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