When you’re faced with a system of equations, you often feel paralyzed and don’t know where to start. You may feel like you’re supposed to use one of the seven virtues or skills for solving these kinds of problems. While there is some truth to this, you need to find a different approach that doesn’t include putting your faith in specific formulas or algorithms. Instead, you should focus on the process and utilize your mathematical intuition to get the right results. This article will teach you four tips for easily solving a system of equations.

## Start At The Beginning

When faced with a system of equations, it’s important to start at the beginning. You can’t expect to solve the equations in the middle of the system because you won’t know what the rest of the equations are. Begin by taking out all the coefficients you don’t need to have and simplify the equations. You can also take a few moments to order the variables so they make sense. For example, in the previous system you would have multiplied the x and y terms but instead of xy you would get x – y or y – x. In the end, it’s all about making the math as easy as possible for yourself so you can avoid any unnecessary confusion when you’re solving the equations. Once you have the basics taken care of, you can then move to the next step.

## Use The Right Operators

The next step is to make use of the appropriate operators. You need to decide if you’re going to have a plus (+) or minus (-) sign in front of each of the coefficients you’re dividing by. If you’re adding or subtracting, then you should use the plus (+) or minus (-) sign before and after each term you’re dividing by. For example, in the third system you would have an x term, a y term, and a z term. If you were adding, you would put a plus before each x, y, and z term and then divide them by 3. Alternatively, if you were subtracting, you would put a minus before each x, y, and z term and then multiply those values by -3. The reason why you need to use the plus or minus sign is because you’re dividing by a number while taking a reciprocal (see below) so if you have a negative number in front of a term, then you’re actually substracting something from that term. Use your best judgement here and make sure you’re consistent throughout the system. If you find that one of the coefficients frequently has a plus or minus sign in front of it, then it’s probably best to subdivide that coefficient into two separate ones.

## Reciprocals

An important concept you need to remember when solving a system of equations is reciprocals. Every equation contains at least one reciprocal which means that the equation can be rewritten to show the same value (or values) in both the numerator and denominator. For example, take the equation (x \+ y) / (x – y) = 3. Here, you would have x \+ y in the numerator and x – y in the denominator so you can see that this is a reciprocal equation. You can therefore divide both sides by (x – y) to get x \+ y / (x – y) = 3. It should be noted that while it’s always best to have at least one reciprocal in your system of equations, you don’t always need to use them. If you feel that the particular set of equations you’re trying to solve don’t have any reciprocals, then it’s probably best not to bother attempting to solve them. Instead, it’s often easier to just rewrite the equations in terms of known variables so you can use existing, known values to solve for the unknowns.

There are two basic rules for using reciprocals. First, whenever you have an x or y term in the numerator, then you should have a plus or minus sign in front of the reciprocal of that term. Second, whenever you have a denominator which contains an x or y term, then you should have a plus or minus sign in front of the reciprocal of that term. These rules should be followed without exception. If you have any questions about what operators to use or if you don’t agree with the rules, then you should probably split one of the coefficients into two or more values.

## Order Of Operations

The order of operations you use when solving a system of equations is important. You need to make sure you perform all the operations in the correct order. The reason for this is that operations in the same group (like adding or subtracting) must be done in the order [plus or minus] * [multiplication or division] * [subtracting or adding]. For example, in the equation (2x \+ 4y) – (x – y) = 11, you would first perform the subtraction and then the addition since those operations are in the same group. The order you perform the operations in affects how the equations will be simplified. For example, if you perform the addition before you perform the subtraction, then that 11 will be reduced to 10 after the subtraction. If you perform the subtraction first, then that 11 will become a 12 since 10 – 5 = 12. Make sure you do all the additions and subtractions before any multiplications or divisions since those are operations which can’t be simplified in the same way subtraction and addition can be. Once you have performed all the necessary operations, then it’s time to solve for the unknown values. If you did everything correctly, then you should end up with the exact same simplified form as the equation you started with. For example, in the previous system you would have (x – y) / 3 = (x \+ y) / 3 so applying this rule gives you x – y = x \+ y which is the same as the equation you started with. This process of simplification is important because you can then solve for the unknown values which will give you a complete picture of what’s going on throughout the entire system. Once you have all the values, then it’s just a matter of substituting them back into the original equation and solve for x and y. If you do everything right, then you should end up with the same values you started with which means you have indeed solved the system of equations correctly.

These four tips for solving a system of equations will help get you started. Remember to start at the beginning and use your mathematical intuition to get the right results. If you found this article valuable, then you should download the complete guide to solving equations PDF for more information on solving systems of equations. Don’t hesitate to come back and visit us in the future since we frequently update our content with helpful tips and examples about various topics related to math and science.