Solving Linear Equation by Graphing

1. Solving Linear Equations by
Graphing
Lesson 2

2. Ideas to Learned
• What are the different possible solutions to
system of linear equation?
• How to classify systems of linear equation?
• How to solve system of linear equation by
graphing?

3. What are the different possible solutions to
system of linear equation?
• Consistent
– A system of linear equation that has at least one
solution
• Inconsistent
– A system of linear equation that does not have a
solution

4. What are the different possible solutions to
system of linear equation?
• Dependent
– A system of linear equation that has infinite
number of solution
• Independent
– A system of linear equation that has exactly one
solution

5. POSSIBLE SOLUTION
NUMBER OF
SOLUTIONS
CONSISTENT 1 or more
INCONSISTENT 0
DEPENDENT Infinite
INDEPENDENT Only 1

6. COMBINATION OF THE SOLUTIONS
• CONSISTENT AND INDEPENDENT
– One solution

7. COMBINATION OF THE SOLUTIONS
• CONSISTENT AND DEPENDENT
– Infinite solution

8. COMBINATION OF THE SOLUTIONS
• INCONSISTENT
– None

9. HOW TO CLASSIFY SYSTEMS OF
LINEAR EQUATION?
• In terms of slope-intercept form y = mx + b:
– If their slopes are different, then the system is
consistent with independent equations and has a
single solution
m1 ≠ m2
– If their slopes are equal and the y-intercepts are
also equal, then the system is consistent with
dependent equations and has infinite solutions.
m1 = m2 and b1 = b2

10. HOW TO CLASSIFY SYSTEMS OF
LINEAR EQUATION?
– If their slopes are equal with different y-
intercepts then the system is inconsistent and has
no solution.
m1 = m2 and b1 ≠ b2

11. Given
Type of
solution
No. of solution
m1 ≠ m2
Consistent and
independent
1
m1 = m2
b1 = b2
Consistent and
dependent
infinite
m1 = m2
b1 ≠ b2
Inconsistent 0

12. HOW TO CLASSIFY SYSTEMS OF
LINEAR EQUATION?
• In terms of standard form ax + by = c:
– One solution when
𝒂 𝟏
𝒂 𝟐
≠
𝒃 𝟏
𝒃 𝟐
– Infinite solution when
𝒂 𝟏
𝒂 𝟐
=
𝒃 𝟏
𝒃 𝟐
=
𝒄 𝟏
𝒄 𝟐
– No solution when
𝒂 𝟏
𝒂 𝟐
=
𝒃 𝟏
𝒃 𝟐
≠
𝒄 𝟏
𝒄 𝟐

13. SOLVING LINEAR SYSTEM BY
GRAPHING
1. Graph each equation.
2. Analyze the graph of the linear system
whether it has one, infinite or no solution.
3. Check the solution in both equations.