Question

On solutions of simultaneous linear equations
Solve the following simultaneous equations.

3x - 4y = 10
4x+3y=5​

Answer 1

AnswEr:

$\large\bold{\underline{\sf{Given\: Equation -}}}$

• 3x - 4y = 10

• 4x + 3y = 5

$\rule{150}2$

3x - 4y = 10 ....[Equation 1]

4x + 3y = 5 ....[Equation 2]

$\:\:\:\small\bold{\underline{\sf{\pink{Multiplying\: Equation\;(1)\;by \:3 \:\&\; Equation\;(2)\:by \; 4}}}}$

$\implies$ (3x - 4y = 10) × 3

$\implies$ 9x - 12y = 30 .....[Equation 4]

$\implies$ (4x + 3y = 5) × 4

$\implies$ 16x + 12y = 20 .....[Equation 5]

$\rule{150}2$

$\:\;\small\bold{\underline{\underline{\sf{\pink{Now,\:From \; Equations \;(3) \;\&\;(4)}}}}}$

$\implies\sf 9x -12y = 30$

$\implies\sf 16x + 12y = 20$

$\implies\sf 25x = 50$

$\implies\sf x =\cancel\dfrac{50}{25}$

$\implies\boxed{\sf{x\:=\:2}}$

Substituting the Value of x in Equation 1

$\implies\sf 3x - 4y = 10$

$\implies\sf 3(2) - 4y = 10$

$\implies\sf 6 - 4y = 10$

$\implies\sf 4y = 6 - 10$

$\implies\sf 4y = -4$

$\implies\sf y = \cancel\dfrac{-4}{4}$

$\implies\boxed{\sf{y\:=\:-1}}$

Hence, The Value of x is 2 & Value of y is -1.

Answer 2

Answer:

x = 2 & y = - 1

Step-by-step explanation:

Given :

3 x - 4 y = 10

Multiply by 3 we get :

9 x - 12 y = 30

= > 12 y = 9 x - 30 .... ( i )

We have also given :

4 x + 3 y = 5

Multiply by 4 we get :

16 x + 12 y = 20

= > 12 y = 20 - 16 x .... ( ii )

From ( i )  and  ( ii ) we get :

= > 9 x - 30 = 20 - 16 x

= > 16 x + 9 x = 20 + 30

= > 25 x = 50

= > x = 2

Putting in x = 2 ( i ) we get :

12 y = 9 x - 30

= > 12 y = 18 - 30  [ x = 2 ]

= > 12 y = - 12

= > y = - 1

Therefore , values of x & y are 2 and - 1 respectively.