Ayden went into a grocery store and bought 2 apples and 6 peaches, costing a total of $7. daniel went into the same grocery store and bought 10 apples and 3 peaches, costing a total of $8. write a system of equations that could be used to determine the price of each apple and the price of each peach. define the variables that you use to write the system.

2 x + 6 y =  7,   10 x + 3 y =  8 is the system of equation.

Here, x = Cost of 1 apple,  y = cost of 1 peach in the grocery store

Step-by-step explanation:

Let the cost of 1 apple in the grocery store  = $x

The cost of 1 peach in the store = $y

Ayden bought 2 apples and 6 peaches

Now, The cost of 2 apples  = 2 times (cost of 1 apple)  = $2x

and   The cost of 6 peaches  = 6 times (cost of 1 peach)  = $6y

Total amount paid by Ayden = $7

⇒ The cost pf 2 apples + Cost pf 6 peaches  = $7

or, 2x + 6 y =  7

Similarly:

Daniel bought 10 apples and 3 peaches

Now, The cost of 10 apples  = 10 times (cost of 1 apple)  = $10x

and   The cost of 3 peaches  = 3 times (cost of 1 peach)  = $3y

Total amount paid by Daniel = $8

⇒ The cost of 10 apples + Cost of 3 peaches  = $8

or, 10x + 3 y =  8

So, the given situation can be represented as system of equations :

2x + 6 y =  7

10x + 3 y =  8

Here, x = Cost of 1 apple,

y = cost of 1 peach in the grocery store

70.30

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0