Consider the system of inequalities and its graph. y ≤ -0.75x y ≤ 3x - 2. In which section of the graph does the actual solution to the system lie?
1, 2, 3, 4

Solution:

Given system of inequalities,

y ≤ -0.75x

y ≤ 3x - 2

We need to assign a value for x to check the possible values of y.

Graphing y ≤ -0.75x,

Let y = -0.75x

When x = 0, y = 0

When x = 1, y = -0.75(1) = -0.75

Thus, join the points (0,0) and (1, -0.75) in coordinate plane, 0 ≤  -0.75(0) (true)

So, the shaded region will contain the origin.

Graphing y ≤ 3x - 2

Let y = 3x - 2

When x = 0,

y = 3(0) - 2 = 0 - 2

y = -2

When y = 0, 0 = 3x - 2

3x = 2

x = 2/3

Thus, join the points (0, -2) and (2/3, 0) in coordinate plane, 0 ≤  3(0) - 2 (false)

So, the shaded region won't contain the origin.

Also, ‘≤ ‘ represents the solid line.

Therefore, the actual solution lies in the fourth quadrant.

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Consider the system of inequalities and its graph. y ≤ -0.75x y ≤ 3x - 2. In which section of the graph does the actual solution to the system lie?

Summary:

Consider the system of inequalities and its graph. y ≤ -0.75x y ≤ 3x - 2. The actual solution to the system lies in the fourth quadrant.