To solve the equation [tex]\( 6x - 2y = 10 \)[/tex] for [tex]\( y \)[/tex], we can follow these steps:
1. Start with the given equation:
[tex]\[
6x - 2y = 10
\][/tex]
2. To isolate [tex]\( y \)[/tex], first move the [tex]\( 6x \)[/tex] term to the right side of the equation. Subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[
-2y = -6x + 10
\][/tex]
3. Now, to solve for [tex]\( y \)[/tex], divide both sides by [tex]\(-2\)[/tex]:
[tex]\[
y = \frac{-6x + 10}{-2}
\][/tex]
4. Simplify the right side by dividing each term individually by [tex]\(-2\)[/tex]:
[tex]\[
y = \frac{-6x}{-2} + \frac{10}{-2}
\][/tex]
5. Simplify the fractions:
[tex]\[
y = 3x - 5
\][/tex]
Therefore, the correct solution is [tex]\( y = 3x - 5 \)[/tex].
The correct answer is:
C. [tex]\( y = 3x - 5 \)[/tex]
