Question

Which ordered pairs make both inequalities true? Check all that apply.

y < 5x + 2

y > x + 1





(–3, 2)


(–1, 3)



(0, 2)


(1, 2)


(2, –1)


(2, 2)

Answer 1

(1,2) and (2,2) makes true

Explanation:

y < 5x + 2

y >=1/2(x) + 1

(–3, 2)

Plug in the ordered pair (x,y) in each inequality

2 < 5(-3) + 2 -----> false

(–1, 3)

3< 5(-1) + 2 --------> false

(0, 2)

2 < 5(0) + 2 -------> false

(1, 2)

2 < 5(1) + 2 ---------> True

2 >=(1/2)1 + 1 ----------->True

(2, –1)

-1 < 5(2) + 2 ---------> True

-1>= (1/2)(2) + 1 -----------> false

(2, 2)

2 < 5(2) + 2 ---------> True

2>= (1/2)(2) + 1 -----------> True

Answer 2

(1,2) and (2,2) since blue is a solid line

Explanation:

To prove if a point satisfies the inequalities,find the point in the point that both inequalities overlap. In the picture, this is colored purple (both pink and blue/purple).