Question

Solve 3x+2y=4, 2x-3y=7 by substitution method

Answer 1

AnswEr:

$\sf{Given\: Equation: 3x + 2y = 4 \:\&\; 2x - 3y = 7}$

$\sf{3x + 2y = 4 \;\:\:\:\:\;\;\;\;\;\;\;....[Equation\:1]}$

$\sf{2x - 3y = 7 \;\:\:\:\:\;\;\;\;\;\;\;....[Equation\:2]}$

$\sf{\;\;\;\:From Equation \;(1)}$

$\implies\sf 3x + 2y = 4$

$\implies\sf 2y = 4 - 3x$

$\implies\sf y = \dfrac{4 -3x}{2}\;\;\;\;\;.....[Equation \;3]$

$\small\bold{\underline{\underline{\sf{Substituting\:the \; Value\: of \; y \: in \; Equation\; (2)}}}}$

$\implies\bf 2x - 3y = 7$

$\implies\sf 2x - 3\bigg(\dfrac{4 - 3x}{2}\bigg) = 7 \:\;\; \; \bigg[ y = \dfrac{4 - 3x}{2}\bigg] \\ \\ \implies\sf 2x - \dfrac{12}{2} + \dfrac{9x}{2} = 7 \\ \\ \implies\sf 2x - 6 + \dfrac{9x}{2} = 7 \\ \\ \implies\sf \dfrac{4x + 9x}{2} = 7 + 6 \\ \\ \implies\sf \dfrac{13}{2}x = 13 \\ \\ \implies\sf x = 13 \times \dfrac{2}{13} \\ \\ \implies\sf \cancel\dfrac{26}{13} \\ \\ \implies\boxed{\bf{x\:=\; 2}}$

$\rule{150}3$

$\small\bold{\underline{\underline{\sf{Substituting\:the \; Value\: of \; x \: in \; Equation\; (3)}}}}$

$\implies\sf 3x + 2y = 4$

$\implies\sf 3(2) + 2y = 4$

$\implies\sf 6 + 2y = 4$

$\implies\sf 2y = 4 - 6$

$\implies\sf 2y = -2$

$\implies\sf y = \cancel\dfrac{-2}{\:\;2}$

$\implies\boxed{\bf{y = -1}}$

$\bold{\underline{\sf{Hence,\; The \: Value\; of \: x \:\& \; y \: is \; 2 \; \&\; -1.}}}$

Answer 2

$\tt{\huge{\orange {-------- }}}$

QUESTION :

Solve 3x+2y=4, 2x-3y=7 by substitution method..

SOLUTION :

Equation 1 :

3x + 2y = 4

Equation 2 :

2x - 3y = 7

=> 2x = 3y + 7

=> x = 3/2 y + 7 / 2

Substituting this value in Equation 1

=> 3 [ 3/2 y + 7 / 2 ] + 2y = 4

=> 9/2 y + 21 / 2 + 2y = 4

=> 9 y + 4 y + 21 = 8

=> 13y = - 13

=> y = -1

=> X = 3 / 2 × ( -1 ) + 7 / 2

=> X = 2

Answer :

Solving we get the following values :

X = 2

Y = -1