Answer
Graph each inequality on the same plane.
Step 1:
Convert the inequality to an equation by replacing inequality by \[=\] sign.
For example, equation: \[y\le mx+c\]
\[y=mx+c\]
Step 2:
Graph the equations using intercept form or slope-intercept form. Find x-intercept and y-intercept for each equation.
Draw a line joining the intercepts, \[\left( 0,y \right)\] and\[\left( x,0 \right)\].
The line is solid or dashed depending on the inequality sign in each.If the inequality contains ≤, ≥symbol, line is solid and if it contains symbol, line is dashed.
Step 3:
Choose a test point from any one of the half-plane. The origin \[\left( 0,0 \right)\]serves the best choice, as it becomes easy to substitute 0 for the variables.
If the statement is true, graph contains the test point. If false, graph does not contain the test point.
If the line passes through origin, use inequality symbol to shade the region. If \[y>mx+c\], shade above the line, or shade below the line.
To solve the system algebraically, the inequalities must be converted into linear equations as in graphical method. The inequality system becomes system linear equation. Use the method of addition or substitution to solve the system.
Back substitute the ordered-pair obtained by solving the inequalities to check if the pair satisfies the inequalities.
