Question

solve the following simultaneous equations:

3x-4y=10; 4x+3y=5

Answer 1

3x-4y = 10

Multiply 3 on both sides

9x-12y =30........(1)

4x +3y=5

Multiply 4 on both sides

16x +12y =20........(2)

Adding (1) and (2), we get

25x =50.

→x=2

Now , putting x = 2 in (1)

18 -12y =30

→-12y = -48

→y =4.

Thus,

x=2;and

y=4

Answer 2

Step-by-step explanation:

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.