Question

Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2

Answer 1

Answer:

Step-by-step explanation:

Given the two inequalities:

$y \ge 2x + 1\\ y \le 2x - 2$

To graph them, first of all, let us write their corresponding equations:

$y = 2x + 1 \\y = 2x - 2$

We now find at least 2 points each which satisfy the equations to plot the graph.

Equation $y = 2x + 1$:

Putting x = 0, y = 1

Putting y = 0, x = $-\frac{1}2$.

Two points are (0, 1) and ($-\frac{1}2$, 0).

Equation $y = 2x -2$:

Putting x = 0, y = -2

Putting y = 0, x = 1.

Two points are (0, -2) and (1, 0).

Now, let us plot them.

Let us take a point (1, 4) and check whether it satisfies the first inequality.

$4 \ge 2 \times 1 +1\\\Rightarrow 4 \ge 3$

Which is true.

So, The shaded region will be towards point (1,4).

Let us take a point (1, 4) and check whether it satisfies the second inequality.

$4 \le 2 \times 1 -2\\\Rightarrow 4 \le 0\ [\bold{False}]$

So, The shaded region will be opposite to point (1,4).

Please refer to the attached graph for the answer.

No solution exists for them because there is no common shaded region.