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:

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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 SOLUTION

y = 3

1x – 6 ( , )

Check solution:

2) 2y = -6x – 4 SOLUTION

y = x + 6 ( , )

Check solution:

3) y =

31

x + 2 SOLUTION

6y – 2x = -6 ( , ) Check 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 < 5

2x + 2

Check solution:

5) y – 3x ≤ -1 2y ≥ 8x – 6 Check solution:

Systems of Equations and Inequalities 6) 3x + 4y ≥ -12

y < -4

1x + 1

Check solution:

7) 3x + 5y ≥ -10

y < -5

3x – 3

Check solution: