Problem 1
Plug (x,y) = (0,0) into the inequality
y < (2/3)x + 2
0 < (2/3)*0 + 2
0 < 0 + 2
0 < 2
The last inequality is true so we do shade the entire region that has the origin in it. In other words, the origin is in the shaded region. For this function, the origin is below the boundary line so the shaded region is below the line
Answer: choice D
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Problem 2
x = number of liters of fruit syrup
y = number of liters of water
"The total number of liters of syrup (x) and water (y) is 7 liters" so x+y = 7 which leads to y = -x+7
This graph is the line through (0,7) and (7,0). Every choice seems to have this graph shown.
"Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup" so we have the equation
3x = 2y+6
which solves to
y = (3/2)x - 3
This line goes through the points (0,-3) and (2,0)
Choice D looks cut off but it looks like choice D is the answer as its the only one with (0,-3) on the line
