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

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

2 thoughts on “Solve by Elimination<br />Method<br />3x +2y = 20<br />5x-3y =8<br />​”

  1. GIVEN :

    • [tex]\bf{3x +2y = 20}[/tex] and [tex]\bf{5x-3y = 8}[/tex]

    TO DO :

    • Solve by Elimination Method.

    SOLUTION:

    Multiply the first equation by 3 :

    [tex]\implies{ \sf3(3x + 2y) = 20 \times 3} \\ \\[/tex]

    [tex]\implies{ \bf9x +6y = 60 – (i)}[/tex]

    Multiply the second equation by 2 :

    [tex]\implies{ \sf 2(5x – 3y) = 8 \times 2} \\ \\[/tex]

    [tex]\implies{ \bf 10x -6y = 16 – (ii)}[/tex]

    Now, Adding both equations :

    [tex] \implies \sf(9x + 6y) + (10x – 6y) = 60 + 16 \\ \\[/tex]

    [tex]\implies \sf9x + 6y + 10x – 6y = 76 \\ \\ [/tex]

    [tex]\implies \sf9x + 10x + \cancel{6y }- \cancel{6y }= 76 \\ \\ [/tex]

    [tex]\implies \sf9x + 10x = 76\\ \\[/tex]

    [tex]\implies \sf19x = 76 \\ \\[/tex]

    [tex]\implies \sf x = \cancel{\dfrac{76}{19} } \\ \\ [/tex]

    [tex]\implies \huge{ \underline{\boxed{ \purple{\tt {x = 4 }}}}} [/tex]

    Substituting the obtained value of x in the first equation :

    [tex]\implies \sf3x + 2y = 20 \\ \\ [/tex]

    [tex]\implies \sf3 \times 4 + 2y = 20 \\ \\[/tex]

    [tex]\implies \sf12 + 2y = 20 \\ \\ [/tex]

    [tex]\implies \sf 2y = 20 – 12 \\ \\ [/tex]

    [tex]\implies \sf 2y = 8 \\ \\ [/tex]

    [tex]\implies \sf y = \cancel{\dfrac{8}{2}} \\ \\[/tex]

    [tex]\implies\huge{ \underline{\boxed{ \purple{ \tt {y = 4 }}}}}[/tex]

    [tex]\huge{\green{\therefore}}[/tex] 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

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