Page 81 - Algebra

4.5. Solving System of Inequalities
A system of inequalities is simultaneously solving more than 2 inequalities together. For example,
x – 6y > 10 3x + 2y ≤ 4
You can solve a system of inequalities using the graphical method. Let us solve a system of inequalities using a graph.
x–y≥6
x + y≤3
Solve both the equations in term of y
x – y ≥ 6 and – y ≥ –x + 6
y≤x–6
Plot y = x – 6 and y = 3 – x on the graph.
Draw a solid line because the inequality has an = sign. Now, use (5, –6) to solve the inequality
y ≤ x – 6 and y ≤ 3 – x
–6 ≤ 5 – 6 and –6 ≤ 3 – 5 –6 ≤–1 and –6 ≤ –2
6 ≥ 1 and 6 ≥ 2
It does satisfy the inequalities.
Now, shade the regions for both the equations. The graph looks like the following:
x + y ≤ 3 y ≤ 3 – x
Page 80 of 177
Algebra I & II