Question

The coordinate grid shows points A through K. What point is a solution to the system of inequalities?


`y \leqslant - 2x + 10 \\ y > (1)/(2)x - 2`
A. a
B.b
C.j
D.h​

Answer 1

A

Explanation:

Answer 2

A. A

Explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

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`y\leq-2x+10`

Draw the solid line
`y=-2x+10`.

Shade region below the line.

for x = 5

`y=-2(5)+10=-10+10=0\to(5,\ 0)`

for x = 0

`y=-2(0)+10=0+10=10\to(0,\ 10)`

`y>(1)/(2)x-2`

Draw the dotted line
`y=(1)/(2)x-2`

Shade region above the line.

for x = 0

`y=(1)/(2)(0)-2=0-2=-2\to(0,\ -2)`

for x = 4

`y=(1)/(2)(4)-2=2-2=0\to(4,\ 0)`

Look at the picture

The solutions: A, C, D, K