Which system of equations is satisfied by the solution shown in the graph? a. x + 2y = 6 and x − y = 10 b. x + y = 6 and x − 2y = 10 c. x + 2y = 10 and x − y = 6 d. x + y = 6 and x − y = -10

In order to find correct system for the given graph, we need to find the slopes and y-intercepts of the lines in shown graph.

For red line we have y-intercept = 10 because it is cutting y-axis at 10.

And slope of the red line is rise/run = 1/1 that is 1.

Using slope-intercept form y=mx+b

The equation of red line is y=1x +10 or x-y =-10.

For black line we have y-intercept = 6 and slope is rise/run = -1/1 = -1.

The equation of black line is y = -1x + 6  or x+y=6.

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)