Recall that we can graph a linear inequality in two variables in the coordinate plane. Let's apply our knowledge of graphing systems of equations and graphing inequalities in order to graph a system of inequalities.
When two or more different inequalities are to be satisfied together, the solution set is a restricted area where the inequalities overlap. For example, suppose we require $y
The solution region is the intersection of the two half-planes defined by the inequalities.
Note that the boundaries have been drawn as dotted lines. This is because the points that satisfy $y=x+1$y=x+1 do not satisfy the strict inequality $y
Select the inequalities that describe the shaded region.
$x$x$\le$≤$1$1 and $y$y$<$<$3$3
$x$x$<$<$3$3 or $y$y$\le$≤$1$1
$x$x$<$<$3$3 and $y$y$\le$≤$1$1
$x$x$\le$≤$1$1 or $y$y$<$<$3$3
$x$x$<$<$1$1 or $y$y$\le$≤$3$3
$x$x$<$<$1$1 and $y$y$\le$≤$3$3
Sketch a graph of the system of inequalities $x$x$\le$≤$5$5 and $y$y$<$<$3$3.
Select the inequalities that describe the shaded region.
$y$y$\ge$≥$-4x-5$−4x−5 or $y$y$\ge$≥$-3$−3
$y$y$\ge$≥$-4x-5$−4x−5 and $y$y$\le$≤$-3$−3
$y$y$\le$≤$-4x-5$−4x−5 and $y$y$\ge$≥$-3$−3
$y$y$\le$≤$-4x-5$−4x−5 and $-\frac{5}{4}$−54$\le$≤$-3$−3
Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.
Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.