Solve for x and y : x 3 + y 4 = 11 , 5 x 6 - y 3 = - 7

The given equations are: x 3 + y 4 = 11 ⇒ 4 x + 3 y = 132 . . . i and 5 x 6 - y 3 = - 7 ⇒ 5 x – 2 y = - 42 . . . ii On multiplying i by 2 and ii by 3 , we get: 8 x + 6 y = 264 . . . iii 15 x – 6 y = - 126 . . . iv On adding iii and iv , we get: 23 x = 138 x = 6 On substituting x = 6 in i , we get: 24 + 3 y = 132 3 y = 132 – 24 = 108 3 y = 108 y = 36 Hence, the solution is x = 6 and y = 36 .

Solve for x and y : 4 x - 3 y = 8 , 6 x - y = 29 3

The given system of equations are: 4 x - 3 y = 8 … … ( i ) 6 x - y = 29 3 … … ( i i ) On multiplying i i by 3 , we get: 18 x - 3 y = 29 … . ( i i i ) On subtracting i i i from i we get: - 14 x = - 21 x = 21 14 = 3 2 Now, substituting the value of x = 3 2 in i , we get: ( 4 × 3 2 ) - 3 y = 8 6 - 3 y = 8 3 y = 6 - 8 = - 2 y = - 2 3 Hence, the solution x = 3 2 and y = - 2 3

Solve for x and y : 2 x - 3 y 4 = 3 , 5 x = 2 y + 7

The given equations are: 2 x - 3 y 4 = 3 … . . ( i ) 5 x = 2 y + 7 … … . . ( i i ) On multiplying i by 2 and i i by 3 4 , we get: 4 x - 3 2 y = 6 . . . . . i i i 15 4 x = 3 2 y + 21 4 . . . . . . i v On subtracting i v from i i i , we get: 1 4 x = 3 4 x = 3 On substituting x = 3 in i we get: ( 2 × 3 ) - 3 y 4 = 3 1 4 x = 3 4 y = 12 3 = 4 Hence, the solution is x = 3 and y = 4 .

Solve for x and y : 2 x + 5 y = 8 3 , 3 x - 2 y = 5 6

The given equations are: 2 x + 5 y = 8 3 … . . ( i ) 3 x - 2 y = 5 6 … … . . ( i i ) On multiplying i by 2 and i i by 5 , we get: 4 x + 10 y = 16 3 … . . . ( i i i ) 15 x – 10 y = 25 6 … ( i v ) On adding i i i and ( i v ) , we get: 19 x = 57 6 x = 57 19 × 6 = 1 2 On substituting x = 1 2 in i , we get: 2 × 1 2 + 5 y = 8 3 5 y = 8 3 - 1 = 5 3 y = 5 3 × 5 = 1 3 Hence, the solution is x = 1 2 and y = 1 3 .

Solve for x and y : 2 x + 3 y + 1 = 0 7 - 4 x 3 = y

The given equations are: 7 - 4 x 3 = y ⇒ 4 x + 3 y = 7 . . . . . . . i and 2 x + 3 y + 1 = 0 2 x + 3 y = - 1 . . . . . . . i i On subtracting i i from i , we get: 2 x = 8 x = 4 On substituting x = 4 in i , we get: 16 x + 3 y = 7 3 y = ( 7 - 16 ) = - 9 y = - 3 Hence, the solution is x = 4 and y = - 3 .