# Solve by EliminationMethod3x +2y = 205x-3y =8​

Solve by Elimination
Method
3x +2y = 20
5x-3y =8

1. ### ☯GIVEN :

• $$\bf{3x +2y = 20}$$ and $$\bf{5x-3y = 8}$$

### ☯TO DO :

• Solve by Elimination Method.

## ➲SOLUTION:

Multiply the first equation by 3 :

$$\implies{ \sf3(3x + 2y) = 20 \times 3} \\ \\$$

$$\implies{ \bf9x +6y = 60 – (i)}$$

Multiply the second equation by 2 :

$$\implies{ \sf 2(5x – 3y) = 8 \times 2} \\ \\$$

$$\implies{ \bf 10x -6y = 16 – (ii)}$$

Now, Adding both equations :

$$\implies \sf(9x + 6y) + (10x – 6y) = 60 + 16 \\ \\$$

$$\implies \sf9x + 6y + 10x – 6y = 76 \\ \\$$

$$\implies \sf9x + 10x + \cancel{6y }- \cancel{6y }= 76 \\ \\$$

$$\implies \sf9x + 10x = 76\\ \\$$

$$\implies \sf19x = 76 \\ \\$$

$$\implies \sf x = \cancel{\dfrac{76}{19} } \\ \\$$

$$\implies \huge{ \underline{\boxed{ \purple{\tt {x = 4 }}}}}$$

Substituting the obtained value of x in the first equation :

$$\implies \sf3x + 2y = 20 \\ \\$$

$$\implies \sf3 \times 4 + 2y = 20 \\ \\$$

$$\implies \sf12 + 2y = 20 \\ \\$$

$$\implies \sf 2y = 20 – 12 \\ \\$$

$$\implies \sf 2y = 8 \\ \\$$

$$\implies \sf y = \cancel{\dfrac{8}{2}} \\ \\$$

$$\implies\huge{ \underline{\boxed{ \purple{ \tt {y = 4 }}}}}$$

$$\huge{\green{\therefore}}$$ The value of x and y is 4 and 4 respectively.

2. Given : 3x +2y = 20

5x-3y =8

To Find :
Solve by Elimination Method

Solution:

3x +2y = 20       Eq1

5x-3y =8              Eq2

3 * Eq1  + 2 * Eq2  will eliminate  y

=> 9x  + 6y  + 10x  – 6y  =  60  + 16

=> 19x  = 76

=> x =  4

5 * Eq1  – 3 * Eq2  will eliminate  x

=>15x + 10y  – 15x  +9y  = 100 – 24

=>  19y  = 76

=> y  = 4

Hence x = y = 4