Certainly! Let's solve the equation [tex]\( x^2 - y = 1 \)[/tex] for [tex]\( y \)[/tex].
1. Start with the given equation:
[tex]\[
x^2 - y = 1
\][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation:
To do this, we need to move [tex]\( y \)[/tex] to the other side and move 1 to the other side. We can achieve this by adding [tex]\( y \)[/tex] to both sides and then subtracting 1 from both sides:
[tex]\[
x^2 - y + y = 1 + y \implies x^2 = 1 + y
\][/tex]
3. Now, we subtract 1 from both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
x^2 - 1 = y
\][/tex]
4. Rewrite the equation to express [tex]\( y \)[/tex] explicitly:
[tex]\[
y = x^2 - 1
\][/tex]
Therefore, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = x^2 - 1
\][/tex]
Thus, the final answer is:
[tex]\[
y = x^2 - 1
\][/tex]
