Question

Coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3

The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?

2x + y ≤ 10
2x − 4y < 8

A, C, D, K
E, F, G, J
A, C, D, H, K
E, F, G, H, J

Answer 1

`2x+y\leq10\ \ \ |-2x\\y\leq-2x+10\\\\for\ x=2\to y=-2\cdot2+10=-4+10=6\to(2;\ 6)\\\\for\ x=5\to y=-2\cdot5+10=-10+10=0\to(5;\ 0)\\\\2x-4y \ \textless \ 8\ \ \ |-2x\\-4y \ \textless \ -2x+8\ \ \ |change\ the\ signs\\4y \ \textgreater \ 2x-8\ \ \ \ |:4\\y \ \textgreater \ 0.5x-2\\\\for\ x=0\to y=0.5\cdot0-2=-2\to(0;-2)\\\\for\ x=4\to y=0.5\cdot4-2=2-2=0\to(4;\ 0)`

Look at the picture.

Answer: A, C, D, K.