Solving equations for indicated variables - College Level

Solve each of the following formula for the indicated variable:

1. y = mx + b for x
2. 4x – 3y = 12 for y

Solution:

It is important to remember that when asked to solve an equation for an indicated variable that usually means isolate that variable on one side of the equal sign and move everything else to the other side.

1) y = mx + b
In order to solve for x we must try to isolate it by itself on one side of the equation. The first
In this process is to subtract b from both sides of the equation as follows:
y b = mx + b – b
y– b = mx
Now it is time to eliminate m from the right hand side of the equation by dividing both sides
By m as follows:
(y-b)/m = (mx)/m
(y-b)/m = x
we have successfully solved this equation for x.

2) 4x-3y = 12
We must isolate the y on one side to be able to solve the equation. We start by adding y to
Each side of the equation as follows:
4x – 3y + 3y = 12 + 3y
4x = 12 + 3y
Now we must subtract 12 from each side of the equation as follows:
4x – 12 = 12 – 12 +3y
4x – 12 = 3y
Now we must divide each side of the equation by 3 as follows:
(4x-12)/3 = (3y)/3
(4x-12)/3 = y
We can simplify this expression as follows:
(4x)/3 – 12/3 = y
4/3 x – 4 = y

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