Mathematics

For solving each pair of equations, use the method of elimination by equating coefficients :
3x - y = 23
$\dfrac{x}{3} + \dfrac{y}{4}$ = 4

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Given equations :

⇒ 3x - y = 23 ………(1)

⇒ $\dfrac{x}{3} + \dfrac{y}{4}$ = 4 ……(2)

Multiplying equation (1) by 3, we get :

⇒ 3(3x - y) = 3 × 23

⇒ 9x - 3y = 69 ………(3)

Multiplying equation (2) by 12, we get :

⇒ $12\Big(\dfrac{x}{3} + \dfrac{y}{4}\Big) = 4 \times 12$

⇒ 4x + 3y = 48 ………..(4)

Adding equation (3) and (4), we get :

⇒ 9x - 3y + 4x + 3y = 69 + 48

⇒ 13x = 117

⇒ x = $\dfrac{117}{13}$ = 9.

Substituting value of x in equation (1), we get :

⇒ 3 × 9 - y = 23

⇒ 27 - y = 23

⇒ y = 27 - 23 = 4.

Hence, x = 9 and y = 4.

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