Questions: Graph the system of inequalities: x-y ≤ 1 x+2y < 4

Solution Steps

The first inequality \(x - y \leq 1\) can be rewritten as \(y \geq x - 1\). The second inequality \(x + 2y < 4\) can be rewritten as \(2y < -x + 4\), or \(y < -\frac{1}{2}x + 2\).

The line \(y = x - 1\) has a slope of 1 and a y-intercept of -1. Since the inequality is \(y \geq x - 1\), we graph the line \(y = x - 1\) as a solid line and shade the region above the line.

The line \(y = -\frac{1}{2}x + 2\) has a slope of \(-\frac{1}{2}\) and a y-intercept of 2. Since the inequality is \(y < -\frac{1}{2}x + 2\), we graph the line \(y = -\frac{1}{2}x + 2\) as a dashed line and shade the region below the line.

The solution to the system of inequalities is the region where the shaded regions from both inequalities overlap.

Final Answer