Question

complete the following activity to solve the simultaneous equation
5x+3y=9,2x+3y=12​

Answer 1

Answer:

$\sf{The \ value \ of \ x \ is \ -1 \ and \ the \ value}$

$\sf{of \ y \ is \ \dfrac{14}{3}.}$

Given:

• The simultaneous equations are

• 5x+3y=9 and 2x+3y=12

To find:

• The values of x and y.

Solution:

$\sf{The \ given \ simultaneous \ equations \ are}$

$\sf{5x+3y=9...(1)}$

$\sf{2x+3y=12...(2)}$

$\sf{Subtract \ equation (2) \ from \ equation (1)}$

$\sf{5x+3y=9}$

$\sf{-}$

$\sf{2x+3y=12}$

_________________

$\sf{3x=-3}$

$\sf{\therefore{x=\dfrac{-3}{3}}}$

$\boxed{\sf{\therefore{x=-1}}}$

$\sf{Substitute \ x=-1 \ in \ equation (1)}$

$\sf{5(-1)+3y=9}$

$\sf{\therefore{-5+3y=9}}$

$\sf{\therefore{3y=9+5}}$

$\boxed{\sf{\therefore{y=\dfrac{14}{3}}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ x \ is \ -1 \ and \ the \ value}}}$

$\sf\purple{\tt{of \ y \ is \ \dfrac{14}{3}.}}$

Answer 2

Step-by-step explanation:

5x + 3y = 9     => ( 1 )

2x + 3y = 12    => ( 2 )

Using elimination method;

( 1 ) - ( 2 ) :

               

         5x + 3y = 9

      - 2x - 3y = -12

         3x + 0 =  -3  

=>  3x = -3

     x = -3/3

     x = -1

substitute x = -1 in ( 1 )

=>  5x + 3y = 9

    5 (-1) + 3y = 9

     -5 + 3y = 9

      3y = 9 + 5

      3y = 14

      y = 14/3

Therefore x = -1 and y = 14/3