**Elimination method :**

Here we are going to see how to solve any linear equation by using this 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.

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 2^{nd} equation from 1^{st} 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.

**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.

HTML Comment Box is loading comments...

**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**