Solve the equation $3 x+5 y=15$ for $y$.
A. $y=15-3 x$
B. $y=3-\frac{3}{5} x$
C. $y=3(15-3 x)$
D. $y=\frac{5}{3} x-3$
Answer (1)
Subtract 3 x from both sides of the equation: 5 y = 15 − 3 x .
Divide both sides by 5: y = 5 15 − 3 x .
Simplify the expression: y = 3 − 5 3 x .
The solution is y = 3 − 5 3 x .
Explanation
Isolating y We are given the equation 3 x + 5 y = 15 and our goal is to isolate y on one side of the equation. This means we want to rewrite the equation in the form y = ... , where the right side contains only x and constants.
Subtracting 3x First, we subtract 3 x from both sides of the equation to get the term with y by itself: 3 x + 5 y − 3 x = 15 − 3 x
5 y = 15 − 3 x
Dividing by 5 Next, we divide both sides of the equation by 5 to solve for y : 5 5 y = 5 15 − 3 x
y = 5 15 − 3 x
Simplifying the expression Finally, we simplify the expression by dividing each term in the numerator by 5: y = 5 15 − 5 3 x
y = 3 − 5 3 x
Final Answer Therefore, the solution is y = 3 − 5 3 x , which corresponds to option B.
Examples
In real life, this type of equation can be used to model a linear relationship between two variables. For example, suppose you have a budget of $15 to spend on apples and bananas. If apples cost $3 each and bananas cost $5 each, the equation 3 x + 5 y = 15 represents the different quantities of apples ( x ) and bananas ( y ) you can buy. Solving for y allows you to easily determine how many bananas you can buy if you know how many apples you want.
