METHODS OF SOLVING LINEAR EQUATIONS IN TWO VARIABLES
Methods of Solving Linear Equations in Two Variables :
In this section, we will see the methods of solving linear equations in two variables.
General form of linear equation in two variables is ax + by + c = 0
Different methods of solving linear equations
(i) Substitution method
(ii) Elimination method
(iii) Cross multiplication method
(iv) Graphical method
Solving Linear Equations Using Substitution 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
Solving Linear Equations Using Elimination Method
Procedure for elimination method :
- Using the elimination method, we can eliminate any one of the variables by combining both equations.
- We can do elimination if and only if the coefficients are same. If they are different, then we have to make the coefficients as same and then we may continue elimination.
- If the coefficients along with the signs are same, we may do elimination by subtracting both the equations.
- If the signs are different and coefficients are same, then we may do elimination by adding both the equations.
- By applying the value of variable we get from the previous step in either of the equations, we will get the value of the remaining variable.
Solving linear equations using elimination method
Solving Linear Equations Using Cross Multiplication Method
Let us consider the following system of linear equations.
a1x + b1y + c1 = 0
a2x + b2y + c2 = 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
Solving Linear Equations Using Graphical Method
Let the system of pair of linear equations be
a1x + b1y = c1
a2x + b2y = c2
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
After having gone through the stuff and examples, we hope that the students would have understood the method of solving linear equations in two variables.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Algebra word problems
Word problems on trains
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on unit price
Word problems on unit rate
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Double facts word problems
Trigonometry word problems
Percentage word problems
Profit and loss word problems
Markup and markdown word problems
Decimal word problems
Word problems on fractions
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Word problems on ages
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
Profit and loss shortcuts
Times table shortcuts
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6