Question

(05.06)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 negativeThe coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?2x + y ≤ 102x − 4y < 8 aA, C, D, K bE, F, G, J cA, C, D, H, K dE, F, G, H, J

Answer 1

we have a system of inequalities

2x + y ≤ 10 -------> y ≤-2x+10

The solution of the first inequality is the shaded area below the solid line y=-2x+10

2x − 4y < 8 ----> -4y <-2x+8 -----> y> (1/2)x-2

the solution of the second inequality is the shaded area above the dashed line

y=(1/2)x-2

Remember that

If an ordered pair is a solution to the system of inequalities, then the ordered pair must lie on the shaded region of the solution of the system

Using a graphing tool

the solution is the shaded region

therefore

D, A, C are solutions

Verify k and H

If an ordered pair is a solution, then must satisfy both inequalities

Verify point K(2,3)

inequality 1

3 ≤-2(2)+10

3≤6 ----> is true (satisfy inequality 1)

Inequality 2

3> (1/2)(2)-2

3>-1 -----> is true (satisfy inequality 2)

that means

point K is a solution too

Verify point H(-4,-4)

Inequality 1

-4≤-2(-4)+10

-4≤18 ---> is true (satisfy inequality 1)

Inequality 2

-4> (1/2)(-4)-2

-4>-4 ----> is not true (not satisfy the inequality 2)

therefore

point H is not a solution

therefore

the answer is

D, A, C, K

option a