Systems of Linear Inequalities
Standard
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane...and graph the solution...to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Solving a system of linear inequalities is very similar to solving linear equations.
- Graph normally like a linear equation.
- Remember to use a dotted or solid line accordingly.
- Shade the inequalities. Where they overlap is the solution.
Example
Graph the system of equations:
y > x - 2
y ≤ -x + 1
Here's y > x - 2 graphed. Remember, plot your y-intercept and from that point, apply your slope!
We use the dotted line because of the > symbol.
We shade above the line because y needs to be greater. You can also plug in a coordinate from the shaded region to double check!
Here's y ≤ -x + 1 graphed. The y-intercept is 1 and the slope is -1/1, which is down 1 and to the right 1.
We use the solid line because of the ≤ symbol.
We shade below the line because y needs to be less than or equal. Try (0,0) to check that the shaded region is correct!
Here's the two systems of inequalities on the same graph
Where they overlap are the solutions to the system of inequalities!