Answer:
Explanation:
Given a graph showing two solid lines that cross in an X pattern with the left quadrant shaded, you want to know the system of equations that is being graphed.
Lines
The answer choices tell you that the boundary lines have equations ...
The boundary lines on the graph are solid, so they are included in the solution set. Both inequalities will include the "or equal to" case. (This eliminates choices B and C.)
Shading
The shading on the graph is to the left of each line, where x-values are less than those on the line. The shading is above the line with positive slope.
To tell where the shading is for a given inequality, look at the inequality symbol and a variable with a positive coefficient. (Coefficient and constant values do not matter for the purpose of determining shading.)
- y > . . . . shading is above the dashed line. Shaded y-values are greater than those on the line.
- y ≤ . . . . shading is below the solid line
- ≥ x . . . . shading is left of the solid line (equivalent to x ≤ )
- x ≥ . . . . shading is right of the solid line
Knowing how the shading works, you can reject choice D:
- y ≤ 3x -1 . . . . shading will be below (to the right of) this line
- x +3y ≥ 6 . . . . shading will be above (to the right of) this line
That is, for this system of equations, the shading would be in the right quadrant of the X where the lines cross.
System of inequalities
The system of inequalities you're looking for is the one shown in the attachment (choice A). These have shading to the left of the solid line in both cases:
- ≥ x . . . . . from y ≥ 3x -1
- x ≤ . . . . . from x +3y ≤ 6