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Mathematics

Solve the following pair of linear equations by the elimination method and the substitution method :
3x + 4y = 10 and 2x - 2y = 2

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Given,

3x + 4y = 10 ……..(1)

2x - 2y = 2 ………(2)

Multiplying equation (2) by 2, we get :

4x - 4y = 4 ………..(3)

Adding equation (1) and equation (3), we get :

⇒ 3x + 4y + 4x - 4y = 10 + 4

⇒ 7x = 14

⇒ x = $\dfrac{14}{7}$

⇒ x = 2.

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

⇒ 3(2) + 4y = 10

⇒ 6 + 4y = 10

⇒ 4y = 10 - 6

⇒ 4y = 4

⇒ y = $\dfrac{4}{4}$

⇒ y = 1.

Hence, x = 2 and y = 1.

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