Algebraic equations have variables like 'x' and 'y' which are to be found by solving them using usual mathematical methods. One such kind of method is to solve equations using elimination method. The simple procedure to follow in case of elimination is to eliminate one variable to solve for another. So now let’s understand how to solve with elimination?
Let’s consider an example of two Algebraic Equations: 25x + 72y = 20 and 36y – 51x = 4.
To solve these equations first rewrite the equations to line up the variables: 25x + 72y = 20 and -51x – 36y = 4.
Proceed further with the elimination process by eliminating either the variable 'x' or variable 'y'. In example we have considered it is easier to eliminate variable 'y'. Multiply first equation by a factor 1 and bottom equation by 2. So, equations now are: 25x + 72y = 20 and -102x + 72y = 8.
Subtract the second equation from the first: (25x + 72y = 20) – (- 102x + 72y = 8). We get equation in terms of 'x' variable, as 'y' variable term with coefficient 72 gets cancelled. So, we are left with 127x = 12 or x = (12 / 127). Now to solve for 'y', substitute the value of 'x' in any equation, say we put value in first equation:
25 * (12 / 127) + 72y = 20,
or y = (280 / 127 * 9),
To verify your answer put values of both 'x' and 'y' in any of two equations. Say we put value of 'x' and 'y' in 2nd equation:
-51 * (12 / 127) + 36 * (280 / 127 * 9) = 4,
Or, - (612 / 127) + (1120 / 127) = 4,
Or, 4 = 4,
Hence, our values for 'x' and 'y' are correct.