Question

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

Answer 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.

Answer 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

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