Inequalities Question 6

y \leq 5x-3

2x-4 \geq 12+y

In the $xy$ -plane, point $A$ is contained in the graph of the solution set of the system of inequalities above. Which of the following could be the coordinates of point $A$ ?

(-4,2)

(1,1)

(3,-10)

(6,2)

Approach

The primary way to approach this question is to test the points. For the point to be contained in the solution set, it must satisfy both inequalities.

\colorbox{aqua}{$(-4,2)$}

2 \leq 5(-4)-3

2 \leq -23   ✖

2(-4)-4 \geq 12+2

-12 \geq 14   ✖

\colorbox{aqua}{$(1,1)$}

1 \leq 5(1)-3

1 \leq 2   \checkmark

2(1)-4 \geq 12+1

-2 \geq 13   ✖

\colorbox{aqua}{$(3,-10)$}

-10 \leq 5(3)-3

-10 \leq 12   \checkmark

2(3)-4 \geq 12+(-10)

2 \geq 2   \checkmark

\colorbox{aqua}{$(6,2)$}

2 \leq 5(6)-3

2 \leq 27   \checkmark

2(6)-4 \geq 12+2

8 \geq 14   ✖