Question

How do you graph the system `y<= 2x + 3` and `x > 1`?

Answer 1

Draw the lines (initially dashed) for `y=2x+3` and for `x=1`.
Shade that section that included by inequalities.
Convert the dashed line along this section corresponding to `y=2x+3` into a solid line.

Explanation:

Step 1: draw dashed line for `y = 2x+3`
Evaluate `y = 2x+3` for a couple of values of `x`,
for example `x=0 rarr y= 3` and `x=2 rarr y=7`
Draw the (dashed) line through the corresponding points on the Cartesian plane.

Step 2: draw dashed line for `x=1`
Draw a vertical (dashed) line through `x=1`.

Step 3: Identify the section included in both inequalities
Test a few `(x,y)` pair values until you identify a pair that is valid for both inequalities.
For example `(x,y) = (2, 0)` satisfies both inequalities, since
`color(white)("XXXX")` `(0) < 2(2) +3` and `(2) > 1`

Step 4: Shade the section which includes the point that satisfies both inequalities

**Step 5: Convert the dashed line segment bordering the shaded area that corresponds to `y = 2x+3` into a solid line to show that it is included in the relation `y <= 2x +3`