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

2. We will solve systems of linear equations by graphing.
Learning Objective
We will solve systems of linear equations by graphing.
CFU

3. Lesson Vocabulary systems of linear equations
solution of a system of linear equations

4. Concept Development– Notes #1
A system of linear equations is a set of two or more linear equations containing two or more variables.
CFU

5. Concept Development
– Notes #2 & 3
2.A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system.
3. So, if an ordered pair is a solution, it will make both equations true.
CFU

6. Concept Development – Notes #4
If an ordered pair does not satisfy the first equation in the system, there is no reason to check the other equations.
Helpful Hint

7. Skill Development Review – Notes #5
Tell whether the ordered pair is a solution of the given system.
2x + 5y = 8
(–1, 2);
3x - 2y = 5
2x + 5y = 8
3x - 2y = 5 –
8 8  8
2(-1)+5(2) 5
3(–1) – 2(2) 
Substitute –1 for x and 2 for y.
The ordered pair (–1, 2) makes one equation true, but
not the other. (–1, 2) is not a solution of the system.
CFU

8. Skill Development Review–
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

9. Concept Development – Notes #6 & 7
6. All solutions of a linear equation are on its graph.
7. 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

10. In other words, you need their point of intersection.
Concept Development
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

11. Concept Development
Sometimes it is difficult to tell exactly where the lines cross when you solve by graphing. Check your answer by substituting it into both equations.
Helpful Hint
CFU

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

13. Skill Development/Guided Practice – Notes #9
Solve the system by graphing. Check your answer.
Graph the system.
x + y = 0
Rewrite the first equation in slope-intercept form. 
y = -x
y = -x
(2) -(–2)
2 2 
The solution is (–2, 2).
CFU

14. Skill Development/Guided Practice – Notes #10
Solve the system by graphing. Check your answer.
y = x – 3
Graph the system.
y = -x - 1
The solution appears to be (1, -2).
Check Substitute (1, -2) into the system.
y = x – 3
– 3
-2 -2 
y = -x -1
-2 –1 -1
-2 -2 
The solution is (1,-2).
CFU

15. 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
(2, 5)
CFU