On this webpage "Elimination method steps" we are going to see how to solve linear equations in elimination method in a easy way.

By using the below flow chart you can easily understand the elimination method steps.

**Problem 1:**

Solve by elimination method

3 x + 4 y = -25

2 x - 3 y = 6

**Solution:**

To eliminate y,let us check the coefficients of y term

3 x + 4 y = -25 ---- (1)

2 x - 3 y = 6 ---- (2)

Since the coefficients of y terms are not same,we have to find the common number for 3 and 4. The common number for 3 and 4 is 12.

To make the coefficients of y as 12,we have to multiply the first equation by 3 and the second equation by 4

(1) x 3 => 9 x + 12 y = -75

(2) x 4 => 8 x - 12 y = 24

Since the symbols of y terms are different,we have to add them to eliminate y

(3) + (4) 9 x + 12 y = -75

8 x - 12 y = 24

-------------------

17 x = - 51

x = -51/17

x = -3

substitute 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

We can also verify the solution which we have found by applying these values in any of the given original equation

3 (-3) + 4 (-4) = -25

-9 - 16 = -25

- 25 = -25

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.

**Problem 2:**

Solve the following system of linear equations by elimination method

x + 2 y = 7

x – 2 y = 1

**Solution:**

X + 2 y = 7 --------- (1)

X – 2 y = 1 --------- (2)

For that let us consider the coefficients of x and y in both equation.

In the first equation we have + 2y and in the second equation we have -2y and the symbols are not same so we can easily eliminate the variable y by just adding two equations.

Adding (1) and (2) we get

X + 2 y = 7

X – 2 y = 1

-------------

2 x = 8

x = 8/2

x = 4

now we have to apply the value of x in wither given equations to get the value of another variable y

Substitute x = 4 in the first equation we get

4 + 2 y = 7

2 y = 7 – 4

2 y = 3

y = 3/2

Solution:

x = 4

y = 3/2

**verification:**

x + 2 y = 7

4 + 2(3/2)= 7

4 + 3 = 7

7 = 7

**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**

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