Solve the following system of simultaneous linear equations by the substitution method:

2x + 3y = 9

3x + 4y = 5

Given,

2x + 3y = 9 ……(i)

3x + 4y = 5 …….(ii)

Solving eqn. (i) we get,

⟹ 2x + 3y = 9

⟹ 2x = 9 - 3y

⟹ x = $\dfrac{9 - 3y}{2}$

Substituting above value of x in eqn. (ii) we get,

$\Rightarrow 3\Big(\dfrac{9 - 3y}{2}\Big) + 4y = 5 \\[1em] \Rightarrow \dfrac{27 - 9y}{2} + 4y = 5 \\[1em] \Rightarrow \dfrac{27 - 9y + 8y}{2} = 5 \\[1em] \Rightarrow 27 - y = 10 \\[1em] \Rightarrow y = 27 - 10 = 17.$

Solving for x,

$x = \dfrac{9 - 3y}{2} = \dfrac{9 - 3(17)}{2} \\[1em] = \dfrac{9 - 51}{2} \\[1em] = \dfrac{-42}{2} \\[1em] = -21.$

Hence, x = -21 and y = 17.