Question

How would i solve this?
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

@SolomonZelman

Answer 2

@Hero @charlotte123 @allie_bear22 @shrutipande9 @lovatic4life please help.

Answer 3

can you change
2x + y ≤ 10
to y ≤ m x + b form ?

Answer 4

subsitute each point for x and y in the equationfrom the question then look which points make the equation true

Answer 5

\[y \le 10 + 1?\]

Answer 6

10x*

Answer 7

2x + y ≤ 10
add -2x to both sides

y ≤ -2x + 10

at x=0 , y =10
at x = 1, y = 8
I would plot those 2 points (0,10) and (1,8) and draw a line through them
can you do that ?

Answer 8

or try point x=2, y - 6 (2,6)
(0,10) looks like it is not on your graph.

Answer 9

notice that the point (0,0) in your equation
y ≤ -2x + 10
gives
0 ≤ 10
which is true. That means all points on the *left* side of that line (or on the line) are part of the solution.

Answer 10

now do the same thing for

2x - 4y < 8

add +4y to both sides
2x < 4y + 8
add -8 to both sides
2x - 8 < 4y
divide both sides by 4
½ x - 2 < y

now plot that line

Answer 11

all points to the right (or above) that second line are part of the solution
look for all the points between the 2 lines.

Answer 12

But what would it be though...i do not understand?

Answer 13

See http://www.khanacademy.org/math/trigonometry/systems_eq_ineq/systems_inequalities_precalc/v/graphical-system-of-inequalities