One equation with a single variable can be solved and the value of the unknown variable can be found out. If there is more than one equation, with different variables then it is known as the system of equations. To solve system of equations, different methodscan be used. The most common methods used in solving system of equations is the Substitution method and the Addition/ Elimination method. Using these methods, the unknown variables in the system of equations can be calculated.
Example 1: Solve the given system of equations: x + 2y = 5 and x + y = 3.
In Substitution method, either ‘x’ or ‘y’ can be chosen to be written in terms of the other.
Given x+ 2y = 5 -> x= 5 – 2y
Now substitute this value of ‘x’ in the second equation, x+ y = 3.
This gives: 5- 2y+ y = 3 -> 5 – y = 3 -> y= 5- 3
This gives: y= 2.
Now x= 5- 2y -> x= 5– 4->x= 1.
Hence the values of the variables are: x= 1 and y= 2.
Example 2: Solve the given system of equations: x + y= 10 and x - y = 4.
In Addition/ Elimination method, one of the variables ‘x’ or ‘y’ is eliminated by adding or subtracting the given two equations accordingly.
Hence, here we can add the right sides of the two equations and the left sides of the two equations.
This gives: (x+ y) + (x – y) = 10 + 4
Hence ‘y’ gets cancelled or eliminated -> 2x = 14 -> x = 7.
Therefore, x+ y = 10 -> 7+ y= 10 -> y = 3.