Two linear equations in two variables can be solved using the substitution techniques, graphical method or by the elimination method.
Let us consider any two real world linear equations in two variables.
x - y = 0
x + y = 4
Now let us first solve them by substitution method:
equation 1 can be written as : x = y ,
Now we substitute this value of x in the second equation:
x + y = 4
or, y + y = 4
or, 2y = 4
or, y = 2
At x = 2 , y = 2. Hence the solution is (2,2)
Now let us solve by elimination method:
adding equation 1 and 2 we get:
x - y = 0
x + y = 4
2x = 4
or, x =2
at x=2 , y = 4-2 =2 Hence the solution is (2,2)
Now we will solve the equations graphical method.
In the graph attached below we can clearly see that the straight line representation of the two equations intersect at the point (2,2)
Hence the solution is (2,2) .
Therefore any linear equation in 2 variables can be solved by substitution , elimination and graphically.
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