Solve the following systems of simultaneous linear equations by the me

1.	Solve the following systems of simultaneous linear equations by the method of substitution x + 2y = – 1, 2x – 3y = 12.
Answer» The given equations are x + 2y = – 1 ..(i) and 2x – 3y = 12 …(ii) From (i) x = – 1 – 2y …(iii) Substituting this value of x in (ii), we get 2( – 1 – 2y) – 3y = 2 ⇒ – 2 – 4y – 3y = 12 ⇒ – 7y = 14 ⇒ y = -2 Putting y = – 2 in (iii), we get x = -1-2×(-2) = -1+4 = 3 Hence the required solution is x = 3 and y = – 2.

Solve the following systems of simultaneous linear equations by the method of substitution x + 2y = – 1, 2x – 3y = 12.

Answer»

The given equations are

x + 2y = – 1 ..(i)

and 2x – 3y = 12 …(ii)

From (i) x = – 1 – 2y …(iii)

Substituting this value of x in

(ii), we get

2( – 1 – 2y) – 3y = 2

⇒ – 2 – 4y – 3y = 12

⇒ – 7y = 14

⇒ y = -2

Putting y = – 2 in (iii), we get

x = -1-2×(-2) = -1+4 = 3

Hence the required solution is x = 3 and y = – 2.