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

Answer 1

The answer should be answer A. (A,C,D,K)

You can easily figure this out by just looking at the graph.  Just look at all points that are in the blue region(overlapping shaded area) and see all the points inside.

H is not included because it falls on the dotted line.  Any point that falls on a dotted line does not satisfy both inequalities.

If the line were solid however, then the point would satisfy both inequalities.  This is because the line would include the greater than or equal to symbol "≥" which means that the point could equal to 8 or be less than 8.  Since the symbol is not used, it doesn't satisfy both equations.

Answer 2

Answer:

A,C,D, and k

Step-by-step explanation:

We are given that a coordinate grid plotted with points A(-5,4), point B(4,7), C(-2,7), D(-7,1),E(4,-2),F(1,-6),G(-3,-10),H(-4,-4),I(9,3) , J(7,-4) and K(2,3).

$2x+y\leq 10$

$2x-4y$

We have to find the points which are solutions of the given  system of inequalities.

Substitute A (-5,4) in equations

$2(-5)+4=-6$

$2(-5)-4(4)=-10-16=-26$

Substitute the value of point B(4,7)

$2(4)+7=15>10$

Point B does not satisfy the first inequality equation.

Now, substitute the value of point C(-2,7)

$2(-2)+7=3$

$2(-2)-4(7)=-4-28=-32$

Now, substitute the value of point D(-7,1)

$2(-7)+1=-13$

$2(-7)-4(1)=-18$

Now, substitute the value of point E(4,-2)

$2(4)-2=8-2=6$

$2(4)-4(-2)=8+8=16>8$

Point E satisfied the first inequality but it does not satisfied the second inequality.Therefore, it is not a solution of system of inequalities.

Now, substitute the value of point F(1,-6)

$2(1)-6=-4$

$2(1)-4(-6)=2+24=26>8$

Point F satisfied the first inequality but it does not satisfied the second inequality.Therefore, it is not a solution of system of inequalities.

Now, substitute the value of point G (-3,-10)

$2(-3)-10=-16$

$2(-3)-4(-10)=34>8$

Point G  satisfied the first inequality but it does not satisfied the second inequality.Therefore, it is not a solution of system of inequalities.Now, substitute the value of point H(-4,-4)

$2(-4)-4=-12$

$2(-4)-4(-4)=-8+16=8=8$

Point H satisfied the first inequality but it does not satisfied the second inequality.Therefore, it is not a solution of system of inequalities.

Now, substitute the value of point I (9,3)

$2(9)+3=21>10$

$2(9)-4(3)=18-12=6$

Point I  satisfied the second  inequality but it does not satisfied the first inequality.Therefore, it is not a solution of system of inequalities.

Now, substitute the value of point  J(7,-4)

$2(7)-4=10=10$

$2(7)-4(-4)=14+16=30>8$

Point J satisfied the first inequality but it does not satisfied the second inequality.Therefore, it is not a solution of system of inequalities.

Now, substitute the value of point K(2,3)

$2(2)+3=7$

$2(2)-4(3)=4-12=-8$

Hence, the point A,C,Dand K are the solutions of given system of inequalities because these points satisfied both inequalities.