At what value of x do the graphs of the equations below intersect? 2x − y = 6 5x + 10y = −10 −2 2

The solution to the equation is: (x,y) = (2,-2) If that helps

Step-by-step explanation:

// Solve equation [1] for the variable  y  

 [1]    y = 2x - 6

// Plug this in for variable  y  in equation [2]

  [2]    5x + 10•(2x-6) = -10

  [2]    25x = 50

// Solve equation [2] for the variable  x  

  [2]    25x = 50  

  [2]    x = 2  

// By now we know this much :

   x = 2

   y = 2x-6

// Use the  x  value to solve for  y  

   y = 2(2)-6 = -2  

Solution :

{x,y} = {2,-2}

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)