Question

solve the following simultaneous equation : 2x-1y=16; 3x-2y=3​

Answer 1

Given :

• 2x - y = 16
• 3x - 2y = 3

To Find :

The x and y.

Solution :

Here we have to form two equations and solve them simultaneously to get the value.

Explanation :

2x - y = 16 --------- (eq.(i))

3x - 2y = 3 --------- (eq.(ii))

Multiplying eq.(i) with 2 and eq.(ii) with 1 we get,

4x - 2y = 32 --------- (eq.(iii))

3x - 2y = 3 --------- (eq.(iv))

Adding eq.(iii) and eq.(iv) we get,

⇒ 4x + 3x = 32 + 3

⇒ 7x = 35

⇒ x = 35/7

⇒ x = 5

∴ x = 5.

Putting x = 5 in eq.(i),

⇒ 2x - y = 16

⇒ 2(5) - y = 16

⇒ 2 × 5 - y = 16

⇒ 10 - y = 16

Transposing 10 in RHS,

⇒ -y = 16 - 10

⇒ -y = 6

∴ y = -6.

The value of x is 5 and y is -6.

Verification :

Putting x = 5 and y = -6 in eq.(i),

⇒ 2x - y = 16

⇒ 2(5) - (-6) = 16

⇒ 10 + 6 = 16

⇒ 16 = 16

∴ LHS = RHS.

• Hence verified.