Question

which of the following points show a solution to the simultaneous inequalities y>1/2x+5 and y<-2x+1?

a. (-5,5)
b. (-1.6,4.2)
c. (4,8)
d. (1,5.5)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which points are solutions to the simultaneous inequalities, we substitute the x and y values of each point into the inequalities.

For option a: (-5,5)
y > 1/2x + 5
5 > 1/2(-5) + 5
5 > -2.5 + 5
5 > 2.5

y < -2x + 1
5 < -2(-5) + 1
5 < 10 + 1
5 < 11

Option a is not a solution to the simultaneous inequalities.

For option b: (-1.6,4.2)
y > 1/2x + 5
4.2 > 1/2(-1.6) + 5
4.2 > -0.8 + 5
4.2 > 4.2

y < -2x + 1
4.2 < -2(-1.6) + 1
4.2 < 3.2 + 1
4.2 < 4.2

Option b is not a solution to the simultaneous inequalities.

For option c: (4,8)
y > 1/2x + 5
8 > 1/2(4) + 5
8 > 2 + 5
8 > 7

y < -2x + 1
8 < -2(4) + 1
8 < -8 + 1
8 < -7

Option c is not a solution to the simultaneous inequalities.

For option d: (1,5.5)
y > 1/2x + 5
5.5 > 1/2(1) + 5
5.5 > 0.5 + 5
5.5 > 5.5

y < -2x + 1
5.5 < -2(1) + 1
5.5 < -2 + 1
5.5 < -1

Option d is also not a solution to the simultaneous inequalities.

Therefore, none of the given options represent solutions to the simultaneous inequalities y > 1/2x + 5 and y < -2x + 1.