1. Tie to LO Activating Prior Knowledge – 1. y – 2x = 1 2. 3x + 3y = 6
Write each expression in slope-intercept form and graph the line.
1. y – 2x = x + 3y = 6
y = 2x + 1
y = -x + 2
Tie to LO

2. Learning Objective
We will solve systems of linear equations by graphing. (You may want to use graph paper for these notes)
CFU

3. Concept Development Review
A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system.
CFU

4. Concept Development Review
So, if an ordered pair is a solution, it will make both equations true.
CFU

5. Skill Development Review–
How can you tell whether the ordered pair is a solution of the given system?
x – 2y = 4
(2, –1);
3x + y = 6
x – 2y = 4
3x + y = 6
Substitute 2 for x and –1 for y.
2 – 2(–1) 4 
4 4
3(2) + (–1) 6
6 – 1 6
5 6
The ordered pair (2, –1) makes one equation true, but not the other.
(2, –1) is not a solution of the system.
CFU

6. Concept Development – Review
1. All solutions of a linear equation are on its graph.
2. To find a solution of a system of linear equations, you need a point that each line has in common.
In other words, you need their point of intersection.
CFU

7. Concept Development - Review
In other words, you need their point of intersection.
y = 2x – 1
y = –x + 5
The point (2, 3) is where the two lines intersect and is a solution of both equations, so (2, 3) is the solution of the systems.
CFU

8. Skill Development/Guided Practice – Notes #3
Solve the system by graphing. Check your answer.
2x + y = - 1
Graph the system.
x - y = 5
Check
Substitute (–2, 3) into the system.
The solution appears to be at (–2, 3).
y = -2x-1
(3) -2(–2)-1 
y = x + 5
3 (–2) + 5 
3 3
The solution is (–2, 3).
CFU

9. Skill Development/Guided Practice – Notes #4
Solve the system by graphing. Check your answer.
Graph the system.
y = x - 3
y = -x - 1
y = -x - 1
y = x - 3
(-2) 1-3  
(-2) -1-1
The solution is (1, -2).
CFU

10. Skill Development – CFU Graph the system. X – 3y = 9 2x + y = 4
Solve the system by graphing. Check your answer.
Graph the system.
X – 3y = 9
2x + y = 4
Rewrite the equations in slope-intercept form.
The solution appears to be (3, –2).
CFU

11. Skill Development/Guided Practice – Notes #5
Solve the system by graphing. Check your answer.
x + y = 2
Graph the system.
y = x - 4
The solution appears to be (3, -1).
Check Substitute (3, -1) into the system.
y = -x + 2
-1 -1 
y = x - 4
-1 -1 
The solution is (3,-1).
CFU

12. Skill Development/Guided Practice – Notes #6
Solve the system by graphing. Check your answer.
x – 2y = -4
Graph the system.
y = -x - 1
The solution appears to be (-2, 1).
Check Substitute (-2, 1) into the system.
1 1 
y = -x - 1
1 -(-2)-1 
1 1
The solution is (-2, 1).
CFU

13. Closure – Notes CFU 1. What did we learn today?
2. Why is this important to you?
3. What are you solving for when looking for a solution in a system of linear equations?
4. Solve the system of equations by graphing.
y + 2x = 9
y = 4x – 3
CFU