Question

A student solving a physics problem 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?to find the unknown has applied physics principles and obtained the expression: μkmgcosθ=mgsinθ−ma, where g=9.80meter/second2, a=3.60meter/second2, θ=27.0∘, and m is not given. which of the following represents a simplified expression for μk?

tanθ− ag
to avoid making mistakes, the expression should not be simplified until the numerical values are substituted.
gsinθ−agcosθ
the single equation has two unknowns and cannot be solved with the information given.

Answer 1

To isolate one of the variables, we need to manipulate the equations. In this case, we can isolate 'a' by subtracting 3b from both sides of the equation and then dividing both sides by 2.

Step-by-step explanation:

When solving a physics problem and isolating a variable in two equations, it is easiest when one of the equations has a coefficient of 1. In the given example, we have the two equations:

3a - b = 5

2a + 3b = -4

To isolate one of the variables, such that it appears by itself on one side of the equation, we need to manipulate the equations. Let's isolate 'a' in the second equation:

2a + 3b = -4

Subtract 3b from both sides:

2a = -4 - 3b

Divide both sides by 2:

a = (-4 - 3b) / 2

So, the equation with 'a' isolated is a = (-4 - 3b) / 2.