To find a particular solution for the equation y = 2y + 6 by inspection, we start by simplifying the equation. Rearranging it gives:
y – 2y = 6
Which simplifies to:
-y = 6
From this, we can multiply both sides by -1 to isolate y:
y = -6
Thus, y = -6 is a particular solution to the equation. We can verify this solution by substituting it back into the original equation:
Substituting, we get:
-6 = 2(-6) + 6
This simplifies as follows:
-6 = -12 + 6
And further simplifies to:
-6 = -6
Since both sides of the equation are equal, we have verified that our particular solution y = -6 is correct.