Solve the following formula for the indicated variable.
– 5x – 3y = 13: solve for y.

9514 1404 393

  y = -5/3x -13/3

Step-by-step explanation:

In any "solve for ..." problem, it is useful to start by identifying where the target is and what has been done to it. Here, y is in one term on the left side of the equation and it has had these things done to it:

We want to undo these in reverse order. We undo addition by adding the opposite. We undo multiplication by multiplying by the reciprocal (equivalently, dividing). Whatever we do to one side of the equation, we must also do to the other side.

So, first we add the opposite of -5x to both sides of the equation.

  -5x +5x -3y = 13 +5x

  -3y = 13 +5x . . . . . . . . . collect terms

Next, we undo the multiplication by -3. We can do that by multiplying both sides by 1/(-3) = -1/3.

  (-1/3)(-3y) = (-1/3)(13 +5x)

  y = -5/3x -13/3 . . . . . also we rearranged the terms to standard form

#12 the answer is the third option