Ch6.4 & 6.8 Systems of Equations and Inequalities

Ch6.4_6.8_SystemsOfEquationsAndInequalities.notebook December 07, 2011

Graphy = 2x + 1


Chapter 6.4 and 6.8Systems of EquationsSystems of Inequalities


To graph a line in slope intercept form:

1) plot the yintercept

2) use the slope to find the next point

3) connect the dots

y = 3x + 5

To graph a line in point slope form:

1) identify the point[take opposite #'s from equation]

2) use the slope to find the next point

3) connect the dots

y 2= 2(x + 5)


Graph the following equations


System of Equations2 or more equationsgraphed on the same graph

The solution of the system is the POINT where the lines intersect

y = 2x + 2y = x + 1


y = mx + bGraph the following systems

NOTE: It will be easier if you rewrite equations in slope intercept form


Graphing InequalitiesSame as graphing a line,but now we shade the graph

y < .... dotted line; shaded BELOW

y ≤.... solid line; shaded BELOW

y > .... dotted line; shaded ABOVE

y ≥.... solid line; shaded ABOVE

EXAMPLES

y = mx + bNOTE: rewrite in slopeintercept form


System of Inequalities2 or more inequalitiesgraphed on the same graph

The solution of the system is the REGION where the inequalities overlap

y > 2x + 2y < x + 1


Graph the following systems

Is (1, 2) a solution to the system?

Is (1, 2) a solution to the system?

NOTE: the inequality sign flips when we divide by a negative number

y = mx + b


Find all ordered pairs (x, y)that satisfy the followingconditions

1) x is greater than 12) y is greater than zero3) x + y < 94) x + 3y ≥ 6


HomeworkPage 260 #1 7Page 278 #9 16

Technology

Ch6.4 & 6.8 Systems of Equations and Inequalities