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Graphing
Substitution
Elimination
Linear Inequalities
Vocab
100
y = 2x + 2 y = x - 1
(-3, -4)
100
y = 2 3x + 2y = 10
(2, 2)
100
x + 3y = 5 2x -3y = -8
(-1, 2)
100
What does a dotted line mean when graphing linear inequalities?
> or <
100
Consists of two or more linear equations in the same variables.
System of linear equations (linear system)
200
y = 2x + 4 y = 3x + 2
(2, 8)
200
x + 3y = 2 -x + 2y = 3
(-1, 1)
200
-5y + 8x = -18 5y + 2x = 58
(4, 10)
200
How is graphing systems of inequalities different than graphing systems of equations? (2 things)
Sometimes they use dotted lines and you have to shade for inequalities.
200
The method of solving equations where you add or subtract equations to end up with one variable.
Elimination
300
x = 3 y = 2x + 1
(3, 7)
300
x - 2y = -10 3x - y = 0
(2, 6)
300
3y - 5x = -26 -2y - 5x = -16
(4, -2)
300
How do you know where to shade when solving systems of inequalities?
Test a point in the equations. If it's true, shade toward the point. If false, shade away. Where the shaded regions overlap is your solution.
300
How can you tell if a linear system has infinitely many solutions?
The equations are the same or solving the system provides a true statement with no variables.
400
4x + 2y = 8 2x + y = 4
No solution
400
2x – 3y = –2 4x + y = 24
(5, 4)
400
​ ​​​3x−4y=8 ​18x−5y=10 ​​
(0, -2)
400
y≤x−2 y>−3x+5
Shaded toward the bottom right
400
A linear system with no solution, when the graphs of the equations are parallel
Inconsistent system
500
y = 1/2 x + 2 y = 1/4 x + 4
(8, 6)
500
5x - y = -13 -5x +2y = 24
no solution
500
​ ​4x−9y−2=0 ​12x−5y+38=0 ​​
(-4, -2)
500
2x – 3y < 12 x + 5y < 20 x > 0
Darkly shaded inside triangle
500
A linear system with infinitely many solutions, when the graphs of the equations are the same
Consistent dependent system