Question

Y> 2x+3

y + 3x ≤ 1

Which two points are solution to this systems of inequalities?

A. (0,5)

B. (-5,5)

C. (-1,4)

D. (0,-5)

E. (-3,-3)

Answer 1

Answer: B and C

Explanation:

Substituting the coordinates of each of the points into the first inequality,

A.
`5 > 2(0)+3 \longrightarrow 5 > 3`, so it satisfies the first inequality.

B.
`5 > 2(-5)+3 \longrightarrow 5 > -7`, so it satisfies the first inequality.

C.
`4 > 2(-1)+3 \longrightarrow 4 > 1`, so it satisfies the first inequality.

D.
`-5 > 2(0)+3 \longrightarrow -5 > 3`, so it does not satisfy the first inequality.

E.
`-3 > 2(-3)+3 \longrightarrow -3 > -3`, so it does not satisfy the first inequality.

• Eliminate D and E.

Now, we can substitute the coordinates of options A, B, and C into the second inequality.

A.
`5+3(0) \leq 1 \longrightarrow 5 \leq 1`, so it does not satisfy the second inequality.

B.
`5+3(-5) \leq 1 \longrightarrow -10 \leq 1`, so it satisfies the second inequality.

C.
`4+3(-1) \leq 1 \longrightarrow 1 \leq 1`, so it satisfies the second inequality.

So, the answers are B and C