3.1 graph each of the following problems 1. 2. 3. 4. 5. 6
TRANSCRIPT
3.1Graph each of the following problems
1.
2.
3.
4.
5.
6.
3.1A 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.
Lines intersect at one point:consistent and independent
Lines coincide;consistent and dependent
Lines are parallel;inconsistent
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
GUIDED PRACTICE
From the graph, the lines appear to intersect at (–2, 1).
Graph each system and then estimate the solution.
1. 3x + 2y = -4 x + 3y = 1
2. 4x – 5y = -10 2x – 7y = 4
3x + 2y = -4
2y = -3x - 4
22
3 xy 2
5
4 xy
3
1
3
1 xy
x + 3y = 1
3y = -x + 1
From the graph, the lines appear to intersect at (–5, –2).
-5y = -4x -10
4x – 5y = -10 2x – 7y = 4
-7y = -2x + 4
7
4
7
2 xy
Consistent & Independent Consistent & Independent
GUIDED PRACTICE
From the graph, the lines appear to intersect at (0, –8).
3. 8x – y = 8 3x + 2y = -16
8x – y = 8 3x + 2y = -16
-y = -8x + 8
y = 8x - 8
2y = -3x - 16
82
3 xy
Consistent & Independent
Solve the system. Then classify the system as consistent and independent,consistent and dependent, or inconsistent.
4x – 3y = 8
8x – 6y = 16
4x – 3y = 8
– 3y = -4x + 8
8x – 6y = 16
– 6y = -8x + 16
(the equations are exactly the same)
2x + y = 4
2x + y = 1
the system has no solution
inconsistent.
2x + y = 4 2x + y = 1
(the lines have the same slope)
consistent and dependent.
The system has infinite solutions
3
8
3
4 xy
3
8
3
4 xy
y = -2x + 4 y = -2x + 1
Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
2x + 5y = 6
5y = -2x + 6
4x + 10y = 12
10y = -4x + 12 Same equationInfinite solutions
Consistent and independent
2x + 5y = 6
4x + 10y = 12A.
3x – 2y = 10
3x – 2y = 2B.
2y = – 3x + 10
3x – 2y = 10 Same slope // lines
no solutioninconsistent
3x – 2y = 2
2y = – 3x + 2
C. – 2x + y = 5
y = – x + 2
– 2x + y = 5
5
6
5
2 xy 5
6
5
2
xy
52
3 xy 1
2
3 xy
y = – x + 2y = 2x + 5
(–1, 3)
consistent
independent
C. – 2x + y = 5
y = – x + 2
– 2x + y = 5y = – x + 2
y = 2x + 5
(–1, 3)
consistent
independent
Is (-1,3) the correct solution?
– 2x + y = 5 y = – x + 2
– 2(-1) + (3)= 5
2 + 3 = 5
3 = – (-1) + 2
3 = 1 + 2 ☺☺
HOMEWORK 3.1P.156 #3-10 and board work
No solution
(3, 3)
Infinite solutions
(-1, 1)
5. 2
4
xy
xy
Solve each system of equations by graphing. Indicate whether the system is Consistent- Independent, Consistent-Dependent, or Inconsistent
6. 52
42
xy
xy
462
23
xy
xy42
2
xy
xy7. 8.
1022
6
yx
yx
1833
6
yx
yx9. 10.
xy
xy
82
421
02
32
yx
xy11. 12.
2
42
yx
yx
1222
2
yx
yx13. 14.
63
1
2
32
yx
xy
14
1
2
3
42
yx
yx15. 16.
(-1, 3)
Consistent, independent
5.
no solution
inconsistent,
6.
y = 3x - 2
Infinite solutions
Consistent, dependent
7.(1, 2)
Consistent, independent
8.
9.
y = x + 6y = x + 5
No solutions
Inconsistent
10.
y= -x + 6y = -x + 6
Infinite solutions
Consistent, dependent
11.
y = ½ x
(2, 1)
Consistent, independent
13.
y = -2x + 4y = x - 2
(2, 0)
Consistent, independent
14.
y = -x + 2y = -x + 6
No solutions
inconsistent15.
y = -3x + 2Consistent, dependent
Infinite solutions16.
y = -2x + 4y = 6x - 4
(1, 1)
Consistent, independent
12.
y = 1/2x + 4 Consistent, dependent
Infinite solutions