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Justine and Roy both ordered takeout dinners for their family. Justine paid $15 for three sodas and three burgers. Roy paid $12 for four sodas and two burgers. Equations representing this situation are given below, where x represents the cost of a soda and y represents the cost of a burger. Find out how much it costs to purchase 1 hamburger and 1 soda.

3x+3y=15
4x+2y=12

Respuesta :

Answer:

The cost of 1 soda is  : x = $ 1

The cost of 1 hamburger is : y = $4

Step-by-step explanation:

Here, the given set of equations is:

3 x + 3 y = 15   ........  (1)

4 x + 2 y = 12    ......  (2)

Here, x represents the cost of a soda.

  and y represents the cost of a burger.

Now, solving the given system of equation by ELIMINATION METHOD.

Multiply (1) with 4 and (2) with -3 , we get:

12 x + 12 y = 60   ........  (a)

-12 x  - 6 y = - 36    ......  (b)

Adding both equations,we get:

12 x + 12 y  -12 x  - 6 y = - 36 +  60

or, 6 y = 24

or, y = 34/6  = 4

or, y = 4

Putting the value of y =  4 in (1) , w e get:

3 x + 3 y = 15  ⇒  3 x +  3 (4) = 15

or, 3 x = 15 - 12 = 3

or, x  = 3/ 3  = 1, or x  =  1

Hence, here, the cost of 1 soda is  : x = $ 1

And the cost of 1 hamburger is : y = $4