Solve the following equations by substitution method.

x + 3y = 10; 2x + y = 5

[In substitution method, we have to find value of one variable in terms of the other variable from any one of the two given equations . Then, we will substitute this value in the other equation. By doing this, we will get a equation in one variable which can be solved easily]

x + 3y = 10……(1)

2x + y = 5 …..(2)

From eq(1),

X + 3y = 10

⇒ x = 10 – 3y

Substituting the value of x in eq(2)

2x + y = 5

⇒ 2(10 – 3y) + y = 5

⇒ 20 – 6y + y = 5

⇒ 20 – 5y = 5

⇒ 5y = 20 – 5

⇒ 5y = 15

Substituting value of y in eq(1)

x + 3y = 10

⇒ x + 3×3 = 10

⇒ x + 9 = 10

⇒ x = 10 – 9

⇒ x = 1

Hence,

x = 1, y = 3