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Lunna [17]
3 years ago
15

Rex mixed x liters of fruit syrup with y liters of water to make a fruit punch. Three times the number of liters of water he mix

ed was 6 more than twice the number of liters of syrup he mixed. The total number of liters of syrup and water he mixed was 7 liters. Which graph best shows the number of liters of fruit syrup and water that Rex added to make the fruit punch?

Mathematics
2 answers:
Ilia_Sergeevich [38]3 years ago
8 0

Answer:

the solution is (3,4) (the second one)

Step-by-step explanation:


AlladinOne [14]3 years ago
3 0
<h2>Answer:</h2>

The correct graph is attached to the answer.

The amount of fruit syrup Rex added is: 3 liters

and the amount of water he added is: 4 liters.

<h2>Step-by-step explanation:</h2>

x denote the amount of fruit syrup added and y denote the amount of water added.

It is given that:

Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup he mixed.

i.e. the equation that satisfies this condition is:

         3y=2x+6\\\\i.e.\\\\2x-3y=-6-----------(1)

i.e. the graph of this equation is a line that passes through (-3,0) and (0,2)

Also, The total number of liters of syrup and water he mixed was 7 liters.

Hence, the equation is:

                       x+y=7------------(2)

i.e. the graph of this equality is a line that passes through (7,0) and (0,7)

Also, from equation (2) we have:

x=7-y

Now, on putting this value of x in terms of y in equation (1) we get:

2(7-y)-3y=-6\\\\i.e.\\\\14-2y-3y=-6\\\\i.e.\\\\14-5y=-6\\\\i.e.\\\\14+6=5y\\\\i.e.\\\\5y=20\\\\i.e.\\\\y=4

Also, on putting the value of y in equation (2) we get:

x=3

Hence, the solution to the system of linear equation is:

                 (3,4)

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