The coordinate grid below shows points a through k. what point is a solution to the system of inequalities?

y < −2x + 10
y < 1 over 2x − 2

1. i
2. b
3. a
4. f

Option 4. F

Step-by-step explanation:

we have

----> inequality A

The solution of the inequality A is the shaded area below the dashed line

The slope of the dashed line A is negative m=-2        

The y-intercept of the dashed line A is (0,-10)

The x-intercept of the dashed line A is (-5,0)

----> inequality B

The solution of the inequality B is the shaded area below the dashed line  

The slope of the dashed line B is positive m=1/2

The y-intercept of the dashed line B is (0,-2)    

The x-intercept of the dashed line B is (4,0)        

The solution of the system of inequalities is the shaded area below the dashed line A and below the dashed line B

Remember that

If a point is a solution of the system of inequalities, then the point is in the shaded area of the solution set of the system

using a graphing point

Graph the solution of the system of inequalities

see the attached figure

The solutions point are

E,J,F and G

The point H is not a solution because the line B is a dashed line

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.