Question

Isolating a variable in two equations is easiest when one of them has a coefficient of 1. Let's say we have the two equations 3A−B=5 2A+3B=−4 and want to isolate one of the variables, such that it appears by itself on one side of the equation. Which of the following is an equation with one of the above variables isolated?

Answer 1

Answer:

$B=3A-5$

Explanation:

Variable Isolation

It's a common practice when dealing with equations that we have to isolate one variable in terms of other variables and/or constants. The isolation of the variable usually implies adding, subtracting, multiplying or dividing by constants. The following example shows how to isolate the A:

$2A+3B=-4\\\\2A=-4-3B\\\\\displaystyle A=\frac{-4-3B}{2}$

We are required to find the equation where the variable has a coefficient of 1 and isolate it. The following equation fits into the description:

$3A-B=5$

Isolating B:

$B=3A-5$