Question

Solve the system of equations by substitution.

Answer 1

Given equations:

• x + y = 15 . . . . . . . . (1)

• y = 4x . . . . . . . . . . . (2)

To find :

• value of x

• value of y

Put value of y of second equation (i.e y = 4x) in equation one (i.e x + y = 15)

➞ x + y = 15

➞ x + 4x = 15

➞ 5x = 15

Divide both LHS and RHS by 5

➞ (5x)/5 = 15/5

➞ x/1 = 3/1

➞ x = 3

Now put value of x in equation 2

{Note : value of x can be inserted both in equation 1 and 2}

➞ y = 4x

➞ y = 4 × 3

➞y = 12

Verification :

put value of x and y in equation 1 :

• x + y = 15

• 12 + 3 = 15

• 15 = 15

LHS = RHS

hence verified !

put value of x and y in equation 2 :

• y = 4x

• 12 = 4 × 3

• 12 = 12

LHS = RHS

hence verified !

∴ Value of x and y is 3 and 12 respectedly .

REQUIRED ANSWER :

(x , y) = (3 , 12)

Answer 2

(3, 12)

Explanation:

Given equations:

• Equation 1: x + y = 15
• Equation 2: y = 4x

Substitute Equation 2 into Equation 1 and solve for x:

⇒ x + 4x = 15

⇒ 5x = 15

⇒ x = 15 ÷ 5

⇒ x = 3

Substitute the found value of x into Equation 2 and solve for y:

⇒ y = 4(3)

⇒ y = 12

Therefore, the solution of the system is (3, 12)