Download systems of equations and inequalities

Systems of Equations and Inequalities
Objectives:
…to solve a system of linear equations by graphing
...to solve a system of linear inequalities by graphing
Assessment Anchor:
Not Available at this time.
Vocabulary alert!!
SYSTEM of linear equations (inequalities) – a set of two or
more linear equations (inequalities)
“Any ordered pair that is a solution to EACH
equation (inequality) in the system is
a solution to the system.
NOTES and EXAMPLES
***To solve a system of linear equations:
1. Graph each equation on the same coordinate plane…using ANY
graphing method. (Be as accurate as possible when drawing lines!)
2. Find the solution by looking for the intersection point(s).
3. Check your solution by substituting back into all equations in system.
So…here is what can happen:
1) One solution – from one point of intersection
2) Many (infinite) solutions – lines are the same line
3) No solution – lines are parallel and do not intersect
Systems of Equations and Inequalities
1)
y = -2x + 1
y=
1
x–6
3
SOLUTION
(
,
)
Check solution:
2)
2y = -6x – 4
y=x+6
SOLUTION
(
,
)
Check solution:
3)
y=
1
x+2
3
6y – 2x = -6
Check solution:
SOLUTION
(
,
)
Systems of Equations and Inequalities
MORE NOTES and EXAMPLES
***To solve a system of linear inequalities:
1. Graph each inequality on the same coordinate plane…using ANY
graphing method. (Be as accurate as possible when drawing lines!)
a. Remember…boundary line can be solid or dashed.
b. Remember…SHADE the region containing all the solutions.
2. Find the solution by looking for the overlapping regions.
3. Check your solution by substituting into all inequalities in system.
4)
y > -x + 4
y<
2
x+2
5
Check solution:
5)
y – 3x ≤ -1
2y ≥ 8x – 6
Check solution:
Systems of Equations and Inequalities
6)
3x + 4y ≥ -12
1
4
y<- x+1
Check solution:
7)
3x + 5y ≥ -10
3
5
y<- x–3
Check solution: