Graphing
Substitution
Elimination
Special Cases
Potpourri
100
Hold the graph AND solution up on a white board. x+1=2, y+2=-3
(1,-5)
100
3x+4=y y=10
(2,10)
100
x-y=3 x+y=7
(5,2)
100
Something true about the slopes of a system with no solution.
Same slope
100
What does it mean to be a solution to a system of equations?
The solution to a system of equations is where both lines intersect. It is a coordinate pair that is a solution to BOTH equations.
200
y=1 y=x
(1,1)
200
h=6g-4 h=-2g+28
(4,20)
200
3x-10y=-25 4x+40y=20
(-5, 1)
200
Something true about the slope and y-intercept of a system with many solutions
Both are the same
200
What does it mean when a system is dependent?
Dependent means there are infinitely many solutions. The equations are the same line.
300
y=-2x-12 4x+2y=8
No Solution
300
y=x-2 2x+2y=4
(2,0)
300
2x+4y=8 5x+y=-7
(-2, 3)
300
Name the number of solutions. (Smart Notebook)
None
300
What does it mean when a system is independent?
An independent system has one solution. The equations have different slopes and different y-intercepts.
400
y=-2x+1 y+2x=-3
No Solution
400
4x+y=-2 -2x-3y=1
(-.5, 0)
400
3x+2y=-9 10x+5y=-5
(-1,-3)
400
Name the number of solutions (Smart Notebook #2)
One
400
What does it mean when a system is inconsistent?
Inconsistent systems have no solution. The equations have the same slope but different y-intercepts, making them parallel.
500
3x+4y=12 2x+4y=8
(4,0)
500
The length of a rectangle is 5 cm more than twice the width. The perimeter is 34 cm. Find the dimensions.
(4, 13)
500
3 burritos and 4 tacos cost $11.33, 9 burritos and 5 tacos costs $22.56
Burrito = $2.01 Taco = $1.49
500
State the number of solutions (Smart Notebook #3)
Many
500
How can you tell whether a system is inconsistent, dependent, or independent without solving it?
Look at the slope and y intercept. If both are different, it is independent. If the slopes are the same but the y intercept is different, the system is inconsistent. If the slopes and y intercept are the same, the system is dependent.
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