1. 3.1
WARM-UP
Graph each of the following problems 1. 4. 2. 5. 6. 3.

2. Solve Linear Systems by Graphing
3.1
Solve Linear Systems by Graphing
A system of linear equations is 2 or more equations that intersect at the same point or have the same solution.
You can find the solution to a system of equations in several ways. The one you are going to learn today is to find a solution by graphing. The solution is the ordered pair where the 2 lines intersect.
In order to solve a system, you need to graph both equations on the same coordinate plane and then state the ordered pair where the lines intersect.

3. Consistent – a system that has at least one solution
Classifying Systems
Consistent – a system that has at least one solution
Inconsistent – a system that has no solutions
Independent – a system that has exactly one solution
Dependent – a system that has infinitely many solutions
Lines intersect at one point:
consistent and independent
Lines coincide;
consistent and dependent
Lines are parallel;
inconsistent

4. GUIDED PRACTICE Graph each system and then estimate the solution.
4x – 5y = -10
2x – 7y = 4
3x + 2y = -4
x + 3y = 1
4x – 5y = -10
2x – 7y = 4
3x + 2y = -4
x + 3y = 1
-5y = -4x -10
-7y = -2x + 4
3y = -x + 1
2y = -3x - 4
From the graph, the lines appear to intersect at (–2, 1).
From the graph, the lines appear to intersect at (–5, –2).
Consistent & Independent
Consistent & Independent

5. GUIDED PRACTICE 8x – y = 8 3x + 2y = -16 8x – y = 8 3x + 2y = -16
From the graph, the lines appear to intersect at (0, –8).
Consistent & Independent

6. the system has no solution
Solve the system. Then classify the system as consistent and independent,consistent and dependent, or inconsistent.
2x + y = 4
4x – 3y = 8
8x – 6y = 16
2x + y = 1
2x + y = 4
2x + y = 1
4x – 3y = 8
8x – 6y = 16
y = -2x + 1
y = -2x + 4
– 3y = -4x + 8
– 6y = -8x + 16
(the lines have the same slope)
(the equations are exactly the same)
the system has no solution
inconsistent.
consistent and dependent.
The system has infinite solutions

7. Consistent and independent
Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
2x + 5y = 6
4x + 10y = 12
2x + 5y = 6
4x + 10y = 12 A.
Same equation
Infinite solutions
Consistent and independent
10y = -4x + 12
5y = -2x + 6
3x – 2y = 10
3x – 2y = 2 B.
3x – 2y = 10
3x – 2y = 2
Same slope
// lines
no solution
inconsistent
2y = – 3x + 10
2y = – 3x + 2
(–1, 3)
consistent
independent C.
– 2x + y = 5
y = – x + 2
– 2x + y = 5
y = – x + 2
y = 2x + 5

8. HOMEWORK 3.1 P.156 #3-10 and board work C. – 2x + y = 5 y = – x + 2
(–1, 3)
consistent
independent C.
– 2x + y = 5
y = – x + 2
– 2x + y = 5
y = – x + 2
y = 2x + 5
Is (-1,3) the correct solution?
– 2x + y = 5
y = – x + 2
3 = – (-1) + 2
– 2(-1) + (3)= 5
3 = 1 + 2 ☺
2 + 3 = 5 ☺
HOMEWORK 3.1
P.156 #3-10 and board work

12. (3, 3)
No solution
(-1, 1)
Infinite solutions

13. Consistent, independent 14.
Solve each system of equations by graphing. Indicate whether the system is Consistent- Independent, Consistent-Dependent, or Inconsistent
(-1, 3)
Consistent, independent 5.
no solution
inconsistent, 6. 5. 6. 8.
y = 3x - 2
Infinite solutions
Consistent, dependent 7.
(1, 2)
Consistent, independent 8. 7. 9.
y = x + 6
y = x + 5
No solutions
Inconsistent
10.
y= -x + 6
y = -x + 6
Infinite solutions
Consistent, dependent
10. 9.
11.
y = ½ x
(2, 1)
Consistent, independent
12.
y = 1/2x + 4
Consistent, dependent
Infinite solutions
12.
11.
13.
y = -2x + 4
y = x - 2
(2, 0)
Consistent, independent
14.
y = -x + 2
y = -x + 6
No solutions
inconsistent
14.
13.
15.
y = -3x + 2
Consistent, dependent
Infinite solutions
16.
y = -2x + 4
y = 6x - 4
(1, 1)
Consistent, independent
16.
15.