3х-у≤1

To solve the inequality \( 3x - y \leq 1 \), we can rearrange it to express \( y \) in terms of \( x \):

1. Isolate \( y \): \[ -y \leq 1 - 3x \] \[ y \geq 3x - 1 \]

This shows that the inequality describes a region above (or on) the line \( y = 3x - 1 \).

2. To graph this inequality, follow these steps:

   • First, graph the line \( y = 3x - 1 \). This is a straight line with a slope of 3 and a y-intercept at (0, -1).
   • Since the inequality is \( y \geq 3x - 1 \), you will shade the region above this line.

3. Remember that the line itself is included in the solution set because the inequality is "less than or equal to," so the line is solid.

The solution is the set of all points \((x, y)\) that lie on or above the line \( y = 3x - 1 \).