ELIMINATION METHOD
Elimination method :
Here we are going to see how to solve any linear equation by using this method.
Steps in Elimination Method
In the given linear equations we can eliminate any one of the variables.
The flow chart given below represents, what are the steps to be done in this method.
Elimination method - Examples
Let us consider the example below to understand this topic better
Question 1 :
Solve by elimination method
3 x + 4 y = -25
2 x - 3 y = 6
Solution :
3 x + 4 y = -25 ---- (1)
2 x - 3 y = 6 ---- (2)
Since the coefficients are different, we have to find the common number for 4 and 3.The common number for 4 and 3 is 12.
(1) x 3 => 9 x + 12 y = -75
(2) x 4 => 8 x - 12 y = 24
Since the signs are different, we have to add equation for eliminating y.
(1) + (2) 9 x + 12 y = -75
8 x - 12 y = 24
-------------------
17 x = - 51
x = -51/17
x = -3
Apply x = -3 in the first equation
3 (-3) + 4 y = -25
- 9 + 4 y = -25
4 y = -25 + 9
4 y = -16
y = -16/4
y = -4
Solution :
x = -3
y = -4
By applying the solution in the given equation, we may verify the solution.
3 (-3) + 4 (-4) = -25
-9 - 16 = -25
- 25 = -25
So, we can decide the answer what we got is correct.
Question 2 :
Solve by elimination method
2 x + 3 y = 5
3 x + 4 y = 7
Solution :
2 x + 3 y = 5 ---- (1)
3 x + 4 y = 7 ---- (2)
The coefficients of x and y are different.Since the symbols of x terms and y terms are same, we can eliminate either x or y term.
So, we are going to eliminate "y" for that we have to find the L.C.M for 3 and 4.The L.C.M for 3 and 4 is 12.
(1) x 4 => 8 x + 12 y = 20
(2) x 3 => 9 x + 12 y = 21
Since the signs are same we have to subtract the 2nd equation from 1st equation equation for eliminating y.
(1) - (2) 8 x + 12 y = 20
9 x + 12 y = 21
(-) (-) (-)
-------------------
-1 x = - 1
x = -1/(-1)
x = 1
Substitute x = 1 in the first equation
8 (1) + 12 y = 20
8 + 12 y = 20
12 y = 20 - 8
12 y = 12
y = 12/12
y = 1
Solution :
x = 1
y = 1
By applying the solution in the given equation, we may verify the solution.
8 x + 12 y = 20
8(1) + 12 (1) = 20
20 = 20
So we can decide the answer what we got is correct.
Elimination method worksheet contains some practice questions based on this topic.You can also try that.
Related topics
- Solve by graphing method
- Solve by substitution
- Synthetic Division
- Rational Expressions
- Rational Zeros Theorem
- LCM -Least Common Multiple
- GCF-Greatest Common Factor
- Simplifying Rational Expressions
- Factoring Polynomials
- Factoring a Quadratic Equation
- Factoring Worksheets
- Framing Quadratic Equation From Roots
- Framing Quadratic Equation Worksheet
- Remainder Theorem
- Relationship Between Coefficients androots
- Roots of Cubic equation
- Roots of Polynomial of Degree4
- Roots of Polynomial of Degree5
After having gone through the stuff, we hope that the students would have understood "Elimination method"
Apart from the stuff given above, if you want to know more about "Elimination method", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
OTHER TOPICS
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 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
