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).
2 answers:
Answer:
- 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.
Step-by-step 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 <em>must</em> overlap, hence <em>there must be solutions</em> to the system.
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<em>Comment on last choice</em>
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.
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