To solve the equation [tex]\(-4x + y = 6\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
-4x + y = 6
\][/tex]
2. Isolate [tex]\(y\)[/tex] on one side of the equation:
To do this, you need to add [tex]\(4x\)[/tex] to both sides of the equation. This will help in removing [tex]\(-4x\)[/tex] from the left side:
[tex]\[
y = 6 + 4x
\][/tex]
3. The equation is now solved for [tex]\(y\)[/tex]:
[tex]\[
y = 6 + 4x
\][/tex]
To illustrate how this equation works, let's substitute a specific value for [tex]\(x\)[/tex].
4. Choose a value for [tex]\(x\)[/tex]:
Assume [tex]\(x = 2\)[/tex].
5. Substitute [tex]\(x = 2\)[/tex] into the solved equation:
[tex]\[
y = 6 + 4 \cdot 2
\][/tex]
6. Perform the multiplication:
[tex]\[
y = 6 + 8
\][/tex]
7. Finally, add the numbers together:
[tex]\[
y = 14
\][/tex]
Therefore, when [tex]\(x = 2\)[/tex], the value of [tex]\(y\)[/tex] is [tex]\(14\)[/tex].
So, the general solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[
y = 6 + 4x
\][/tex]
