Final answer:
The correct statements about graphing the inequalities y ≤ -4x+6 and y < 6x + 6 are that the line y = -4x+6 will be solid (A) and shading will be below both the y = -4x+6 and y < 6x + 6 lines(C).
Step-by-step explanation:
When graphing the inequalities y ≤ -4x+6 and y < 6x + 6 on a coordinate grid, the following statements can be evaluated:
- A. True, the line for y = -4x + 6 will be solid because it includes the values where y is exactly -4x + 6 due to the ≤ (less than or equal to) sign.
- B. False, shading will not be between the lines because the inequalities y ≤ -4x + 6 and y < 6x + 6 do not overlap in that manner. Shading for y ≤ -4x + 6 will be below this line and shading for y < 6x + 6 will be below that line as well.
- C. True, shading will be below both lines due to the direction indicated by the inequalities. Where the shaded regions overlap is the solution set to the system of inequalities.
- D. False, as both statements A and C are true.