Question

solve the give equation by the method of substitution

2x+3y=9
3x+4y=9

Answer 1

Step-by-step explanation:

2x=9-3y

x=9-3y/2 ( 1)

sub (1) 3(9-3y/2)+4y=9

y=18

sub y=18 x=45/2

Answer 2

AnSwEr :

⠀⠀⠀⠀⠀⠀⠀ $\large{\boxed{\sf{\red{ x\:=\:-\:9}}}}$

⠀⠀⠀⠀⠀⠀⠀ $\large{\boxed{\sf{\red{ y\:=\:9}}}}$

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SoLuTioN :

• By using substitution method :

$\implies \sf 2x\:+\:3y\:=\:9\:----\: \small {\red{Equation\:1}}$

$\implies \sf 3x\:+\:4y\:=\:9\:----\: \small{\red{Equation\:2}}$

• Now , working on equation 1 :

• $\large \sf x\:=\: \dfrac{9\:-\:3y}{2}$

— Substituting , this is Equation 2 :

• $\sf 3(\dfrac{9\:-\:3y}{2})\:+\:4y\:=\:9$

• $\sf \dfrac{27\:-\:9y}{2}\:+\:4y\:=\:9$

• $\sf \dfrac{27\:-\:9y\:+\:8y}{2}\:=\:9$

• $\sf \dfrac{27\:-\:y}{2}\:=\:9$

• $\sf 27\:-\:y\:=\:18$

• $\sf y\:=\:27\:-\:18$

$\implies \large{\boxed{\sf{\red{ y\:=\:9}}}}$

• Now , To find value of x , substitute value of y in Equation 1 :

• $\sf 2x\:+\:3(9)\:=\:9$

• $\sf 2x\:+\:27\:=\:9$

• $\sf 2x\:=\:9\:-\:27$

• $\sf 2x\:=\:-\:18$

• $\sf x\:=\: \dfrac{18}{2}$

$\implies \large{\boxed{\sf{\red{ x\:=\:-\:9}}}}$

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