Question

The cost of 2kg of apples and 1kg of grapes on the day was found to be 160. After a month ,the cost of 4 kg of apples and 2kg of grapes is 300.Respresent the situation algebraically and geometrically.
CLASS 10 LINEAR EQUATION IN 2 VARIABLES​

Answer 1

Answer:

Let cost each kg of apples  = Rs x

Cost of each kg of grapes  = Rs  y

Given that The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160

So that

2 x +  y            = 160              … (1)

2x                    = 160  - y

x                      =  (160 – y)/2

Let y = 0 , 80  and 160  we get

X         = (160 – ( 0 ))/2         =  80

X         = (160- 80 )/2             = 40

X         = (160 – 2* 80 )/2      = 0

Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300

so we get

4 x +  2 y        = 300              … (2)

Divide by 2 we get

2 x + y             = 150

Subtract 2x both side we get

Y         = 150 – 2 x

Plug  x = 0 , 50 , 100  we get

Y         = 150 – 2*0                = 150

Y         = 150 – 2* 50             = 50

Y         = 150 – 2 * (100 )      = - 50

Algebraic representation

2 x +  y            = 160              … (1)

4 x +  2 y        = 300              … (2)

hope it helps.......sis

Answer 2

x 65 55 45 35

y 20 40 60 80

Let the cost of 1 kg of apples be x and that of 1 kg be y

So the algebraic representation can be as follows:

2x+y=160

4x+2y=300⇒2x+y=150

The situation can be represented graphically by plotting these two equations.

2x+y=160⇒y=160−2x

x 70 60 50 40

y=160−2x 20 40 60 80

2x+y=150⇒y=150−2x

x 65 55 45 35

y=150−2x 20 40 60 80

We can see that the lines do not intersect anywhere, i.e. they are parallel. Hence we can not arrive at a solution.