Question

8) 49x - 57y = 172; 57x - 49 = 252 solve the simultaneous equation​

Answer 1

Answer:

x = 7 and y = 3

Step-by-step explanation:

49x - 57y = 172.............(1)

57x - 49y = 252...........(2)

addition and subtraction of both, we have

106x - 106y =  424 ( addition of 1 & 2)      -8x - 8y = -80 ( subtraction of 1 & 2)

x - y = 4 ............... (3)                                     x  +  y = 10  ......(4)

addition of (3) & (4)

x - y =  4                                substitute x = 7 in equation (4)

x + y = 10                                7 + y = 10

------------                                       y = 10 - 7

2x  = 14                                        y = 3

x = 14/2

x = 7

hence x = 7 and y = 3

Answer 2

Answer:

49x – 57y = 172 .....(I)

57x – 49y = 252 .....(II)

Adding (I) and (II)

49x+57x-57y-49y=172+252

⇒106x-106y=424

⇒x-y=4 .....(III)

Subtracting (II) from (I) we have

49x-57y-57y-(-49y)=252-172

⇒-8x-8y=-80

⇒-x-y=-10

⇒x+y=10 .....(IV)

Adding (III) and (IV)

x-y=4x+y=10⇒2x=14⇒x=7

Putting the value of x = 7 in (IV) we get

7+y=10⇒y=10-7⇒y=3

Thus, (x, y) = (7, 3).