To solve the equation [tex]\( 6x - y = 7 \)[/tex] for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation.
Here are the steps to find [tex]\( y \)[/tex]:
1. Start with the given equation:
[tex]\[
6x - y = 7
\][/tex]
2. To isolate [tex]\( y \)[/tex], we need to get rid of the term [tex]\( 6x \)[/tex] on the left-hand side. We can do this by subtracting [tex]\( 6x \)[/tex] from both sides of the equation:
[tex]\[
-y = 7 - 6x
\][/tex]
3. Now, we have [tex]\(-y\)[/tex] on the left-hand side. To solve for [tex]\( y \)[/tex], we need to multiply both sides of the equation by [tex]\(-1\)[/tex]:
[tex]\[
y = -1 \cdot (7 - 6x)
\][/tex]
4. Simplify the right-hand side:
[tex]\[
y = -7 + 6x
\][/tex]
5. Rearrange the terms to match the standard form [tex]\( y = mx + b \)[/tex]:
[tex]\[
y = 6x - 7
\][/tex]
Thus, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = 6x - 7
\][/tex]
