Marni writes this system to determine how much of each ingredient alyssa plans to buy. she uses x to represent
cups of frozen fruit puree and y to represent cups of yogurt.
x + y = 6,
2x + 3y = 14
to solve this system using the linear combination method, marni multiplies the first equation by -2 to eliminate the x
variable.
-2x - 2y = -12
2x + 3y = 14
finish solving the system to determine how many cups of fruit puree and yogurt alyssa will buy
marni determined that alyssa plans to purchase cups of fruit puree and cups of yogurt

Alyssa buys 4 cups of frozen fruit puree and  2 cups of yogurt.

Step-by-step explanation:

Here, x =  Represent  cups of frozen fruit puree

         y =   Represent cups of yogurt.

The given system of equations by Marni  are:

x + y = 6,

2x + 3y = 14

After first step of elimination,the equations are:

-2x - 2y = -12

2x + 3y = 14

Now, ADD BOTH THE EQUATIONS to eliminate the variable x:

-2x - 2y +  (2x + 3y)   =  -12   + 14

or, y = 2

Now, put y =2 in x + y =6, we get

x = 6 - y = 6 -2 = 4

So, x = 4 and y = 2 is the solution of the given system.

Hence,  Alyssa buys 4 cups of frozen fruit puree and She  buys  2 cups of yogurt.