Question

Which statements are true about the graph of the system of linear inequalities? Check all that apply. y > 3x – 4 y < x + 1 The graph of y > 3x − 4 has shading above a dashed line. The graph of y < x + 1 has shading below a dashed line. The graphs of the inequalities will intersect. There are no solutions to the system. The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

Answer 1

• The graph of y > 3x − 4 has shading above a dashed line.
• The graph of y < x + 1 has shading below a dashed line.
• The graphs of the inequalities will intersect.

Explanation:

y > ... means the shading will be above the corresponding line.

y < ... means the shading will be below the corresponding line.

These lines have different slopes, so the solution spaces must overlap, hence there must be solutions to the system.

_____

Comment on last choice

It isn't clear exactly what is intended by the last offered statement. Both of the listed points are in the solution space of y > 3x-4. Neither point is in the solution space of y < x+1.

Together, the two graphs intersect the entire y-axis. Jointly, they only intersect the y-axis on the interval -4 < y < 1.

The y-intercepts of the two boundary lines are (0, 1) and (0, -4). Neither of these points is in the solution space of the system of inequalities.

Answer 2

1.The graph of y > 3x − 4 has shading above a dashed line.

2.The graphs of the inequalities will intersect.

Explanation:

Which statements are true about the graph of the system of linear inequalities? Select two options.

y > 3x – 4

y < x + 1

The graph of y > 3x − 4 has shading above a dashed line.

The graph of y < x + 1 has shading below a dashed line.

The graphs of the inequalities will intersect.

There are no solutions to the system.

The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).