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

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]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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

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

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

$\implies\sf 25x = 50$

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

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

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:

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

• 3x - 4y = 10

• 4x + 3y = 5

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) ×

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

$\implies$ (4x + 3y = 5) × 4

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

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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

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

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

$\implies\sf 25x = 50$

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

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

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.