There are no solutions to the system of inequalities shown below
y< 4x-6
y> 4x+2

a. true
b. false

Step-by-step explanation:

<, > - dot line

≤, ≥ - solid line

<, ≤ - shading to the left

>, ≥ - shading to the right

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y < 4x - 6 → y = 4x - 6

for x = 0 → y = 4(0) - 6 = 0 - 6 = -6 → (0, -6)

for x = 2 → y = 4(2) - 6 = 8 - 6 = 2 → (2, 2)

y > 4x + 2 → y = 4x + 2

for x = 0 → y = 4(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = -1 → y = 4(-1) + 2 = -4 + 2 = -2 → (-1, -2)

Look at the picture.

NO SOLUTION

Other method:

We have the lines y = 4x - 6 and y = 4x + 2. The slopes of lines are the same. Therefore the lines are parallel.

y < 4x - 6 → shadded to the left from the line

y > 4x + 2 → shadded to right from the line

Shaded regions do not have a common part. Therefore, there are no solutions.

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