Transcript 3.3 Solving Systems of Inequalities by Graphing Pg. 123

3.3 Solving Systems of
Inequalities by Graphing
Pg. 123
Standards addressed: 2.1 & 2.2
Steps for Graphing Inequalities:
1. Write the inequality in slope-intercept form.
2. Use the slope and y-intercept to plot two points.
3. Draw in the line. Use a solid line for less than or equal to ()
or greater than or equal to (). Use a dashed line for less than
(<) or greater than (>).
4. Pick a point above the line or below the line. Test that point in
the inequality. If it makes the inequality true, then shade the
region that contains that point. If the point does not make the
inequality true, shade the region on the other side of the line.
5. Systems of inequalities – Follow steps 1-4 for each inequality.
Find the region where the solutions to the two inequalities
would overlap and this is the region that should be shaded.
Look at the two graphs. Determine the following:
A.
The equation of each line.
B.
How the graphs are similar.
C.
How the graphs are different.
Use a dotted or dashed line when the inequality is < or >
Use a solid line when the inequality is ≤ or ≥
Solutions of Lines Vs. Inequalities
• We can test a solution to a line by picking
a point that is on the line and plugging that
point back into the equation.
• We can test a solution to an inequality by
picking a point that is SOMEWHERE in
the shaded region and plugging that point
into the inequality.
Point: (-4, 5)
Pick a point from the shaded
region and test that point in
the inequality y ≥ x + 3.
Point: (1, -3)
Pick a point from the shaded
region and test that point in
the equation y ≤ -x + 4.
http://www.mathbits.com/MathBits/TISection/
Algebra1/linearinequ2.htm
Systems of Equations
vs.
Systems of Inequalities
• A system of equations will have ONE
point, no points, or an infinite amount of
points for an answer. The SOLUTION is
where the two lines intersect.
• A system of inequalities will have MANY
ordered pairs that satisfy the inequalities.
Heart Rate
Graph the following linear system of inequalities.
y  2x  4
y  3x  2
Use the slope and yintercept to plot two
points for the first
inequality.
y
Draw in the line. For 
use a solid line.
x
Pick a point and test
it in the inequality.
Shade the appropriate
region.
Graph the following linear system of inequalities.
y  2x  4
y  3x  2
y  2x  4
0  2(0) - 4
y
Point (0,0)
0  -4
The region above the line
should be shaded.
x
Now do the same for the
second inequality.
Graph the following linear system of inequalities.
y  2x  4
y  3x  2
Use the slope and yintercept to plot two
points for the second
inequality.
y
Draw in the line. For <
use a dashed line.
x
Pick a point and test
it in the inequality.
Shade the appropriate
region.
Graph the following linear system of inequalities.
y  2x  4
y  3x  2
y
y  3x  2
-2  3(-2) + 2
Point (-2,-2)
-2 < 8
The region below the line
should be shaded.
x
Graph the following linear system of inequalities.
y  2x  4
y  3x  2
y
x
The solution to this
system of inequalities is
the region where the
solutions to each
inequality overlap. This
is the region above or to
the left of the green line
and below or to the left
of the blue line.
Shade in that region.
Graph the following linear systems of inequalities.
1.
y  x  4
yx2
y  x  4
yx2
y
Use the slope and yintercept to plot two
points for the first
inequality.
x
Draw in the line.
Shade in the
appropriate region.
y  x  4
yx2
y
Use the slope and yintercept to plot two
points for the second
inequality.
x
Draw in the line.
Shade in the
appropriate region.
y  x  4
yx2
y
The final solution is the
region where the two
shaded areas overlap
(purple region).
x
Homework:
• Workbook pg. 16 (1-9 – we will start class
next time with number 10.)