1. 3.1 Solving Systems by Graphing or Substitution
Learning Objective: to solve systems using both methods
Warm-up (IN)
1. Write each equation in slope intercept form.
y=x-9
y=2/5x
y=-4/7x+2
y=15x-30
y=3x-3.24

2. Notes
Linear System –
a set of 2 or more equations in 2 or more variables
Solution –
An ordered pair, (x, y), that satisfies all of the equations
Coinciding
parallel
intersecting
Infinitely many solutions
no solutions
One solution

3. Consistent System –
Has at least one solution
Independent System –
Exactly one solution
Dependent System –
Infinitely many solutions
Inconsistent System –
no solutions
***To solve by graphing
1 – Graph both lines
2 – Estimate point where they intersect
3 – Check by plugging the point into the 2 equations

4. EX 1 – solve by graphing and classify the system
Consistent and independent
(-1, 3)
yes
yes

5. ***To solve systems by substitution:
1 – get one variable by itself in one equation
2 – Substitute that expression into the other equation
3 – Solve for the variable
4 – plug that value back into either of the original equations to find the other variable

6. EX 2 – Solve by substitution:
Always write solution as an ordered pair!!!

7. POINT CHALLENGE!
Try this… page 158

8. Out – Explain how to use substitution to solve the system
Summary – today I understood…
HW – p #10-17, 25-30, 40-43