Question

Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6

Answer 1

Answer:

The correct answer is in the image below

Step-by-step explanation:

I hope this helps

Answer 2

Answer:

The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.

Step-by-step explanation:

We know if the sign of inequality contains '=', the graph of the inequality is drawn with the help of a solid line but if the sign of inequality does not contains '=', the line of the graph of inequality is dotted.

For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality $y > 2x+4$, we let the inequality as: $y=2x+4$

Putting y=0, we get: $2x+4=0\\x=-2$

The point will be: (-2,0)

Now, putting x=0, we get: $2(0)+4=y\\y=4$

The point will be: (0,4)

Now as the sign of inequality is >, the line of graph will be dotted.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

$0 > 0+4$

$0 \ngtr 0+4$

So, the shaded region will be away from the test point.

Similarly, finding the points for the inequality $x+y\le6$, we let the inequality as: $x+y=6$

Putting y=0, we get: $x+0=6\\x=6$

The point will be: (6,0)

Now, putting x=0, we get: $0+y=6\\y=6$

The point will be: (0,6)

Now, as the sign of inequality is of $\le$, the line of graph will be solid.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

$0+0\leq6$

$0\le6$

So, the shaded region will be towards the test point.

The resulting graph is attached after the solution.

The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.