SOLUTION: Choose the answer that lists all the quadrants in which the solution points are located for this system of inequalities: 2x + y <= 6 y >= 1 Quadrants 1 and 2 Quadrant

Question 280494: Choose the answer that lists all the quadrants in which the solution points are located for this system of inequalities:
2x + y <= 6
y >= 1
Quadrants 1 and 2
Quadrants 1,2 and 4
Quadrants 2 and 3
Quadrants 2 and 4

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
y >- 1 puts the answer in quadrants 1 and 2.

2x + y <= 6 needs to be converted to get y on the left side of the equation and the x's on the right sides of the equation.

2x + y <= 6 is the original equation.

subtract 2x from both sides of the equation to get:

y <= -2x + 6

if x is 0, this equation becomes y <= 6
if x is 1, this equation becomes y <= 4
y is defiitely in the first quadrant.
if x is -1, this equation becomes y <= 8
y is definitely in the second quadrant.

Looks like your answer will be first and second quadrant.

A graph of both equations is shown below:

The equations are:

y >= 1
y <= -2x + 6

The shaded region is anything on or above the line y = 1, and anything on or below the line y = -2x + 6.

The shaded region is in quadrants 1 and 2.

The shaded region can never be in quadrants 3 and 4 because the value of y has to be greater than 1.
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