Question

What are the solutions to the equation ly - 31 = 2?

1. Rewrite for two solutions: (y-3) = 2,-(y-3) = 2
2. Solve the first equation:
3. Solve the second equation:
-y+3=2
y=5
The solutions to the equation ly - 31= 2 are
and

Answer 1

9514 1404 393

Answer:

y = 1 and y = 5

Explanation:

When rewriting the absolute value equation as two different equations, I like to keep the coefficient of the variable positive. Here, that means writing it as ...

y -3 = ±2

Then adding 3 gives ...

y = 3 ± 2 = {1, 5}

The solutions are y = 1 and y = 5.

_____

Finishing up your solution method, we have ...

2. Solving the first equation, we get y -3 = 2 ⇒ y = 2+3 = 5

3. Solving the second equation, we get -y +3 = 2 ⇒ -y = -1 ⇒ y = 1

The solutions are ...

• y = 5
• y = 1