System of Inequalities

How do you solve the system of inequalities by graphing?
y ≤ 2x + 2
y < -x + 1

Graph each inequality, then the solution would be the overlap of the two half-planes.

To graph y ≤ 2x + 2:

Graph the line y = 2x + 2  {y-intercept is 2 and slope is 2}

Use a solid line, given the less than or equal to sign.
This means the solution to this inequality also includes
the points on the boundary line

Since it is ≤, shade down the y-axis from the boundary line

---

To graph y < -x + 1:

Graph the line y = -x + 1  {y-intercept is 1 and slope is -1}

Use a dash line, given just the less than sign with no equal to.
This means the solution set to this inequality does not include
the points on the boundary line.

Since it is <, shade down the y-axis from the boundary line.


The solution to the system of inequalities {shown below} is the overlap of the two half-planes.

---

The solution set (overlap shown to the left) is the set of points that satisfies both inequalities.

---

- Algebra House