Question

Solve the system of equations using elimination.The graph shows the solution to a system of inequalities:

Solid line joining ordered pairs 0, 3 and 7, 0. Shade the portion of the graph below the line in the first and fourth quadrants.

Which of the following inequalities is modeled by the graph?

2x + 5y ≥ 14; x ≥ 0
2x + 5y ≤ 14; x ≥ 0
2x − 5y ≤ 14; x ≥ 0
−2x − 5y ≤ 14; x ≥ 0

Answer 1

The inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0

This inequality corresponds to the solid line that passes through the ordered pairs (0,3) and (7,0). The line has a slope of -2/5, and it can be written in the form y = (-2/5)x + b, where b is the y-intercept, and it can be calculated as b = (5/2)x + 14. The shading is below the line and in the first and fourth quadrants, which corresponds to the inequality 2x + 5y ≥ 14; x ≥ 0.

The other inequalities provided in the options do not correspond to the graph:

2x + 5y ≤ 14; x ≥ 0, the shading is above the line

2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line

−2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line

So, the inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0