Question

How do you solve multi variable equations?​

Answer 1

To solve multi-variable equations, distinguish between known and unknown variables, select appropriate equations to express unknowns in terms of knowns, and solve these equations, often simultaneously, through algebraic manipulation while carefully verifying each step.

Step-by-step explanation:

To solve multi-variable equations, you need to identify all the unknown variables and the known variables in the problem. Once you have everything labeled, look for an equation or a set of equations that express the unknowns in terms of the knowns. If an equation has only one unknown, you can solve for it directly.

However, if there are multiple unknowns, you will need more than one equation to solve the problem. This could involve solving simultaneous equations, which often requires many algebraic steps. It is vital to carefully check and recheck your work throughout this process to ensure accuracy.

Another useful approach, specifically in physics problems, is to apply the loop rule if applicable. This entails writing an equation for each independent loop in a circuit and then solving these simultaneous equations.

Ultimately, a systematic approach involving determining knowns and unknowns, choosing appropriate equations, and algebraically solving for the unknowns will lead to the solution of multi-variable problems.

Answer 2

1. Understand what multi-variable equations are.

Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.

2. Know that you are trying to figure out the values of the variables, or unknowns.

The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.

• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.

3. Know what a numerical coefficient is.

The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:

• 8 and 3 for the first equation; 5 and 2 for the second equation.


4. Understand the difference between solving with elimination and solving with substitution.

When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).

• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.


5. Understand that there can be linear equations that have three or more variables.

Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.