General form of linear equation in two variables :
ax + by + c = 0
Different methods of solving linear equations :
(i) Substitution method
(ii) Elimination method
(iii) Cross multiplication method
(iv) Graphical method
Step 1 :
In the given two equations, solve one of the equations either for x or y.
Step 2 :
Substitute the result of step 1 into other equation and solve for the second variable.
Step 3 :
Using the result of step 2 and step 1, solve for the first variable.
Examples of solving linear equations using substitution method
Procedure for elimination method :
Solving linear equations using elimination method
Let us consider the following system of linear equations.
a_{1}x + b_{1}y + c_{1} = 0
a_{2}x + b_{2}y + c_{2} = 0
We have to write the coefficients of the equations and do cross multiplication as shown below.
We write the coefficient of y and constant term and two more columns by repeating the coefficients of x and y as follows.
The result is given by
The solution is
Solving linear equations using cross multiplication method
Let the system of pair of linear equations be
a_{1}x + b_{1}y = c_{1}
a_{2}x + b_{2}y = c_{2}
We know that the given two lines in a plane only one of the following may happen
(i) Two lines will intersect at one point
(ii) Two lines will not intersect
(iii) Two lines are coincident
Examples of the solving linear equations using graphical method
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