Question

solve the following sets of simultaneous equations. 3x-5y=16;x-3y=11​

Answer 1

Answer

(x−3y=8)×3

⇒3x−9y=24

(-)3x-5y=16

________

-4y=8 ⇒y=−2

x−3y=8⇒x=3y+8=−6+8=2⇒x=2

solution

Answer 2

Answer:

The solution of the given simultaneous equations is

$\displaystyle{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:\left(\:-\:\dfrac{7}{4}\:,\:-\:\dfrac{17}{4}\:\right)}}}$

Step-by-step-explanation:

The given simultaneous equations are

3x - 5y = 16 & x - 3y = 11.

3x - 5y = 16 - - - ( 1 )

x - 3y = 11 - - - ( 2 )

By multiplying equation ( 2 ) by 3, we get,

3 ( x - 3y ) = 11 * 3

⇒ 3x - 9y = 33 - - - ( 3 )

By subtracting equation ( 1 ) from equation ( 3 ), we get,

3x - 9y - ( 3x - 5y ) = 33 - 16

⇒ 3x - 9y - 3x + 5y = 17

⇒ 3x - 3x - 9y + 5y = 17

⇒ 0 - 4y = 17

⇒ - 4y = 17

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:y\:=\:-\:\dfrac{17}{4}}}}}$

By substituting $\displaystyle{\sf\:y\:=\:-\:\dfrac{17}{4}}$ in equation ( 2 ), we get,

x - 3y = 11 - - - ( 2 )

$\displaystyle{\implies\sf\:x\:-\:3\:\times\:\dfrac{-\:17}{4}\:=\:11}$

$\displaystyle{\implies\sf\:x\:-\:\left(\:\dfrac{-\:51}{4}\:\right)\:=\:11}$

$\displaystyle{\implies\sf\:x\:+\:\dfrac{51}{4}\:=\:11}$

$\displaystyle{\implies\sf\:x\:=\:11\:-\:\dfrac{51}{4}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{11\:\times\:4\:-\:51}{4}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{44\:-\:51}{4}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:-\:\dfrac{7}{4}}}}}$

∴ The solution of the given simultaneous equations is

$\displaystyle{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:\left(\:-\:\dfrac{7}{4}\:,\:-\:\dfrac{17}{4}\:\right)}}}$