Pair of Linear Equations in Two variables — Maths STD 10 — Question

y = 5 .......... (1)
2x - 3y=4 ............. (2)

1. Elimination method:
   Multiplying equation (1) by 2, we get equation (3)
   2x +2y =10 ............. (3)
   2x−3y =4 ........... (2)
   Subtracting equation (2) from (3), we get
   5y =6 ⇒ y = $\frac{6}{5}$
   Putting value of y in (1), we get
   x + $\frac{6}{5}$=5
   ⇒ x =5− $\frac{6}{5}$= $\frac{{19}}{5}$
   Therefore, x = $\frac{{19}}{5}$and y = $\frac{6}{5}$
2. Substitution method:
   x +y =5 .......................... (1)
   2x−3y =4 ......................... (2)
   From equation (1), we get,
   x =5−y
   Putting this in equation (2), we get
   2(5−y )−3y =4
   ⇒ 10−2y−3y =4
   ⇒ 5y =6
   ⇒ y = $\frac{6}{5}$
   Putting value of y in (1), we get
   x =5−$\frac{6}{5}$=$\frac{{19}}{5}$
   Therefore, x = $\frac{{19}}{5}$and y = $\frac{6}{5}$