1.

y gex + 2 2x + 3y le6 In which of the following does the shaded region represent the solution set in the xy-plane to the system of inequalities above?

Answer»




Solution : The solutions of the FIRST inequality, `y ge X + 2`, lie on or above the line y = x + 2, which is the line that passes through (−2, 0) and (0, 2). The second inequality can be rewritten in slopeintercept form by dividing the second inequality, `2x + 3Y le 6`, by 3 on both SIDES, which yields`2/3x + y le2`, and then subtracting`2/3x` from both sides, which yields `y le-2/3 x+2`. The solutions to this inequality lie on or below the line `y = − 2/3x +2`, which is the line that passes through (0, 2) and (3, 0). The only graph in which the shaded region meets these criteria is choice B.
Choice A is incorrect and may result from REVERSING the inequality sign in the first inequality. Choice C is incorrect and may result from reversing the inequality sign in the second inequality. Choice D is incorrect and may result from reversing the inequality signs in both inequalities.


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