Solve the formula Ax+By=C for y.
A. y = C/B + Ax O
B. y = (C – Ax)/B
C. y = (C + Ax)/B
D. y = C – (Ax)/B
The Correct Answer and Explanation is :
The correct answer is B. ( y = \frac{C – Ax}{B} ).
Explanation:
To solve for ( y ) in the equation ( Ax + By = C ), you need to isolate ( y ) on one side of the equation.
Step-by-Step Solution:
- Start with the original equation:
[
Ax + By = C
] - Subtract ( Ax ) from both sides to move the term involving ( x ) to the right side:
[
By = C – Ax
] - Divide both sides by ( B ) to solve for ( y ):
[
y = \frac{C – Ax}{B}
]
Thus, the solution is ( y = \frac{C – Ax}{B} ), which matches option B.
Why This Solution Works
In algebra, isolating a variable requires performing inverse operations to “undo” the terms around the variable you’re solving for. In this case, we’re solving for ( y ), so we need to remove any terms attached to it. Starting with ( Ax ) and ( By = C ), we remove ( Ax ) first by moving it to the other side of the equation. Finally, since ( y ) is multiplied by ( B ), we divide both sides by ( B ) to get ( y ) by itself.
Common Mistakes and Why Other Options are Incorrect
- Option A: ( y = \frac{C}{B} + Ax )
- This mistakenly places ( Ax ) on the right side without subtraction, which doesn’t align with the original equation.
- Option C: ( y = \frac{C + Ax}{B} )
- This incorrectly suggests adding ( Ax ) to ( C ) instead of subtracting it, which changes the original equation’s meaning.
- Option D: ( y = C – \frac{Ax}{B} )
- Here, only ( Ax ) is divided by ( B ), while ( C ) is not, which isn’t correct given the algebraic manipulation needed.
This approach ensures accuracy and is foundational for manipulating equations in algebra.