There is not one but various ways to solve equations easily however the easiest one is elimination method. In it, we eliminate one term to find out the value of other term and then substitute the resulting value in one of the given equation. However, for this method, we need minimum two equations that are subtracted from each other to get the values. Here is the brief concept of solving equations. Elimination method when no multiplication is required When there are two variables in an equation, then we need to isolate any term or use inverse operations to get the number or variable alone. So, let’s understand it with an example 2x – y = -8 and 2x + 2y = 6. Note: keep in mind that while using elimination method signs of the number gets inverse, i.e., negative become positive and vice versa. 2x – y = -8 (-) (2x + 2y = 6) ______________________ (-y) = (-2) Both the minus signs get canceled, and then we get the value of y=2. Elimination method when multiplication is required To inverse terms, sometimes we need to make one variable of both the terms equal so that it gets canceled easily. While solving equations, we tend to multiply both the equations like this: For example 2x – y = 4 and 3x + y = -2 (2x – y = 4)(3) Becomes 6x + 3y = 12 (3x + y = -2)(2) Becomes 6x + 2y = -4 So, here we solve equation the resulting equation: 6x + 3y = 12 (-) (6x + 2y = -4) _________________ y = 16 Important points to be considered while solving equations by elimination method: Take care about signs Signs are the most crucial aspect of equations so consider signs carefully. Along with this, you should have proper knowledge about sign combinations. Like tow minus signs are equal to plus i.e. (-,-=+), (-, +=-), (+,-=-) and (+, +=+). Inverse operations Inverse operations are required in this method as we have to make one variable alone to get the value of another variable. While going for such operations, consider proper signs and numbers for getting the solution right. There is one important tip as isolate consonant to make the variable alone. Substitute values Without substituting values, you can’t get the value of both variables. Also, if you have multiplied the equation to make it inverse then never put the value in the multiplied equation. One needs to put the value in that equation which is organic, i.e., not multiplied. Solving simple equations Talking about simple equations then could be solved via formula or by substituting value. Here is an example of it: 4x + 2 = 10 Step 1: Here combine like terms, i.e., 10 and 2 on the right-hand side and let the term 4x remain on the left-hand side. Now, let’s see how to verify your answer? For that you need to put the value of x in equation 4x + 2 = 10 like this:
4x + 2 = 10 4(2) + 2 =10 8 + 2 =10 10 =10 Important points Equations with exponents and roots need to be simplified at first, for example, 2x(x + 1) = 4 2x(x + 1) = 4 2x² + 2x = 4 (Like this you have to reduce it to the simplest form) Solving equations properly requires perfection which you will get from practice. Keep in mind that the topic is not about approx value, but it is about exact value. So, follow the above guide and solve equations easily.
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